Answers
Answer:
[tex]a^{12} b^{4}[/tex]
Step-by-step explanation:
To simplify we will have to use the negative exponent rule and the power rule along with some algebra.
Negative Exponent Rule
[tex]a^{-b} =\frac{1}{a^b}[/tex]
Power Rule
[tex](a^b)^{c} =a^{bc}[/tex]
Given
[tex](a^{-4}b^{-1}c )^{2} (a^2bc)^{2}[/tex]
Rewrite [tex]a^{-4}[/tex] using negative exponent rule.
[tex](\frac{1}{a^{4}}* b^{-1}c )^{2} (a^2bc)^{2}[/tex]
Rewrite [tex]b^{-1}[/tex] using negative exponent rule.
[tex](\frac{1}{a^{4}}* \frac{1}{b}*c )^{2} (a^2bc)^{2}[/tex]
Simplify
[tex](\frac{c}{a^4b} )^{2} (a^2bc)^{2}[/tex]
Rewrite the base as its reciprocal.
[tex](\frac{a^4b}{c} )^{2} (a^2bc)^{2}[/tex]
Apply the power rule.
[tex]\frac{a^8b^2}{c^2} *(a^2bc)^{2}[/tex]
Apply the power rule.
[tex]\frac{a^8b^2}{c^2} *a^4b^2c^2[/tex]
Cancel the common factor of [tex]c^2[/tex].
[tex]a^8b^2 a^4b^2[/tex]
Apply the power rule.
[tex]a^{12} b^{4}[/tex]
Answer:
[tex]a^{12}\:b^{4}[/tex]
Step-by-step explanation:
Given expression:
[tex]\left(a^{-4}\:b^{-1}\:c\right)^{-2}\left(a^2\:b\:c\right)^2[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies a^{(-4 \times -2)}\:b^{(-1 \times -2)}\:c^{-2}\:a^{(2 \times 2)}\:b^2\:c^2[/tex]
Simplify:
[tex]\implies a^{8}\:b^{2}\:c^{-2}\:a^{4}\:b^2\:c^2[/tex]
Collect like terms:
[tex]\implies a^{8}a^{4}\:b^{2}b^2\:c^{-2}c^2[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies a^{(8+4)}\:b^{(2+2)}\:c^{(-2+2)}[/tex]
Simplify:
[tex]\implies a^{12}\:b^{4}\:c^{0}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^0=1:[/tex]
[tex]\implies a^{12}\:b^{4}(1)[/tex]
[tex]\implies a^{12}\:b^{4}[/tex]
Related Questions
Identify the quotient and the remainder
(24x^3 - 14x^2 + 20x +6)÷(4x^2 - 3x +5)
Answers
The quotient is (6x + 1) and the remainder is (-7x + 1).
What is a factor of a polynomial?
We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given A cubic polynomial 24x³ - 14x² + 20x + 6 divided by 4x² - 3x + 5.
So, (24x³ - 14x² + 20x + 6)/(4x² - 3x + 5).
= (4x² - 3x + 5)(6x + 1) + (-7x + 1)/(4x² - 3x + 5) in rhe form N = DQ + R.
The same applies to the division of polynomials.
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Solutions to quadratic equation 4x^2+5x+1=0
Answers
A rectangular tennis court has a length of 24 m and a width of 11m what is the length of the diagonal court explain how you worked out your answer
Answers
The length of the diagonal of the rectangular tennis court is given as follows:
26.4 meters.
How to obtain the length of the diagonal?The tennis court is rectangular, meaning that the diagonal is the hypotenuse of a right triangle, in which the sides are the length and the width.
Applying the Pythagorean Theorem, the diagonal length can be obtained as follows:
d² = 24² + 11²
d² = 697
[tex]d = \sqrt{697}[/tex]
d = 26.4 m.
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17. Higher Order Thinking In 4th grade,
Richard read 37 books. In 5th grade, he read
9 more books than the year before. This
year, in 6th grade, Richard plans to read at
least 12 more books than the total number
of books read in both 4th and 5th grades.
Richard writes the inequality b≥ 180 to
show the total number of books he will
have read in 4th, 5th, and 6th grades. Is his
inequality correct? Why or why not?
Answers
Step-by-step explanation:
No, Richard's inequality is not correct. In order to determine the correct inequality, we first need to find the total number of books that Richard read in 4th and 5th grade. In 5th grade, he read 9 more books than in 4th grade, so the total number of books he read in 5th grade was 37 + 9 = 46 books. The total number of books he read in 4th and 5th grade is therefore 46 + 37 = 83 books.
Since Richard plans to read at least 12 more books than the total number of books he read in 4th and 5th grade, he needs to read at least 83 + 12 = 95 books in 6th grade. In order to have read at least 180 books in total over 4th, 5th, and 6th grade, his inequality should be b ≥ 180. However, b represents the number of books he plans to read in 6th grade, which means the inequality should be 95 ≥ 180, which is not true. Therefore, Richard's inequality is not correct.
d. Describe the relationship between the 9s in Ithaca's average annual rainfall?
Answers
Precipitation (inches), 2.08, 1.98, 2.64, 3.29; Snowfall (inches), 17.6, 14.2, 11.7, 3.4; The Ithaca Climate Page.
What is the relationship between the patterns in rainfall and temperature?Increased evaporation as a result of rising average temperatures at the Earth's surface leads to more precipitation overall. As a result, many places might expect more precipitation as a result of a hotter environment.Moving from the equator toward the poles results in less precipitation. Because temperature impacts how much moisture air can contain, precipitation often decreases with increasing latitude, with higher precipitation typically occurring at lower latitudes.There is a larger than 28% chance of rain on any given day during the wetter season, which lasts for 6.4 months from April 2 to October 14.June is the month in Ithaca with the most rainy days, with an average of 11.3 days with at least 0.04 inches of precipitation. From October 14 to April 2, the dry season lasts 5.6 months.Tho learn more about Ithaca climate refer to :
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You are eating in a restaurant and have only $20 in your pocket. You are required to tip the service staff 18%. How much money can you spend on food?
Answers
A population of 2 rabbits grows at the rate of 400% every two months. How many
rabbits are in the population after 1 year?
Answers
Answer:
50 rabbits
Step-by-step explanation:
?/2 = 400/100
multiply 2 by 400
2 times 400 = 800
now, divide it by 100
800/100 = 8
every two months = 8 rabits
12 months in a year
12/ 2 equals 6
6 times 8 = 48
+the two begining rabbits
= 50 total rabbits
Consider whether it's wrong or right.
Answers
The solution to the equations are
0 ∈ N is False 7/2 ∈ Q is True
√16 ∈ Q' is False π ∈ Q' is True
3/2 ∈ I is False -3 ∈ R is True
0 ∈ I is True -1 ∈ I⁺ is False
( 1 - 3 ) ∈ N is False 8/2 ∈ I is True
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number be represented as A
Now , the equation will be
a)
Let the number be A = 0
The number 0 is a whole number , rational number and an integer
0 is not a natural number
So , the equation is False
b)
Let the number be A = √16
The value of A = 4
The number 4 is a natural number , whole number , rational number and an integer
4 is not an irrational number
So , the equation is False
c)
Let the number be A = 3/2
The number 3/2 is a rational number
3/2 is not an integer
So , the equation is False
d)
Let the number be A = 0
The number 0 is a whole number , rational number and an integer
0 is an integer
So , the equation is True
e)
Let the number be A = ( 1 - 3 )
The value of A = -2
The number -2 is a rational number and an integer
-2 is not a natural number
So , the equation is False
f)
Let the number be A = 7/2
The number 7/2 is a rational number
7/2 is a rational number
So , the equation is True
g)
Let the number be A = π
The number π is an irrational number
π is an irrational number
So , the equation is True
h)
Let the number be A = -3
The number -3 is a real number
7/2 is a real number
So , the equation is True
i)
Let the number be A = -1
The number -1 is an integer and real number
-1 is a negative integer
So , the equation is False
j)
Let the number be A = 8/2
The value of A = 4
The number 4 is a natural , whole , integer and rational number
4 is an integer
So , the equation is True
Hence , the equations are solved
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Identify the basic shapes in the figure:)
Answers
Answer:
Rectangle and triangle
find the perimeter of a figure
Answers
Answer:
27.72
Step-by-step explanation:
Just sum up all the sides together
What is 15% of 12 meters?
Answers
Answer:
1.8 meters
Step-by-step explanation:
Multiply 12 by 0.15 to get your answer. You multiply because the question says "15% of 12 meters" which means you need to multiply.
Answer: 1.8
Step-by-step explanation:
Multiply 12 by .15 (15% as a decimal), and you'll get 1.8 meters. You multiply, because it says 15% of 12 meters.
Find the product write the product as a mixed number
Answers
Answer:
[tex] \frac{9}{10} \times 54 = \frac{9 \times 54}{10} = \frac{486}{10} = 48 \frac{6}{10} = \frac{243}{5} [/tex]
Complete the equations bellow.
Answers
A car rental company charges a daily fee of $12.95 on all rental cars.
What is the cost for 3 days?
A
$25.90
B
$36.75
С
$38.85
D
$45.23
Answers
Answer:
C
Step-by-step explanation:
Sorry if I’m wrong but I think I’m right
Answer:
answer is C
Step-by-step explanation:
it's just 12.95 times 3
Verena sleeps from 11 p.m. until 9a.m. What fraction of a day does Verena sleep? *
Answers
Kade has $45 in savings and wants to purchase a video game console for $250. He has a coupon for 10% off, and sales tax is 8.25%. In order to be financially responsible, Kade wants to wait until he has enough in savings to not have to borrow money. If Kade is able to save $45 each week, what is the minimum amount of weeks Kade should save before making his purchase?
Answers
Answer:5 weeks
Step-by-step explanation:
Find the surface area of the prism
Answers
Answer:
Step-by-step explanation:
surface area=4×(4×2)+2×(4×4)=32+32=64 m²
HELP ME PLEASE!!! This is my last day
Answers
Answer:
B : 91.25, V: 365 B:12.25, V: 42.875 B:28.4, V: 142B:32.2, V: 293.02Help need answer will give brainliest
Answers
If
f
(
x
)
=
2
x
4
−
3
x
+
3
f(x)=2x
4
−3x+3, then what is the remainder when
f
(
x
)
f(x) is divided by
x
−
1
x−1?
Answers
x
−
1
x−1?x
)
=
2
x
4
−
3
x
+
3
f(x)=2x
4
−3x+3, then what is the remainder when
f
(
x
)
f(x) is divided by
x
−
1
x−1?
According to Okun's law, if output grew 7% and full-employment output rose 5%, what would be the change in the unemployment rate
Answers
Answer:
the change would be 2% of course
The change in the unemployment rate is -1%.
Given to us:
output grew = 7%
full-employment output grew = ΔY = 5%
According to Okun's law,
employment output - 2 (change in the unemployment rate) = output grew
5% - 2(Δu) = 7%
- 2(Δu) = 7% - 5%
- 2(Δu) = 2%
[tex]\bold {\Delta u = \frac{2\%}{-2} }[/tex]
[tex]\bold{\Delta u = -1\%}}[/tex]
Hence, the change in the unemployment rate is -1%.
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If a student deposits $1,500 in the bank and earns an annual interest rate of 8%,
how much will he have after 15 years? (Hint: y = ab)
Answers
Explanation: 1= P x r x t
P is the principal amount, $1500.00.
r is the interest rate, 8% per year, or in decimal form, 8/100=0.08.
t is the time involved, 15....year(s) time periods.
So, t is 15....year time periods.
find the simple interest, we multiply 1500 × 0.08 × 15 to get that
===================================================
Work Shown:
a = 1500 = deposit amountb = 1.08 = represents an increase of 8% since 100% + 8% = 1+0.08 = 1.08The equation y = a*b^x updates to y = 1500*(1.08)^x
Plug x = 15 into the equation to find out how much money you have after 15 years.
y = 1500*(1.08)^x
y = 1500*(1.08)^15
y = 1500*(3.17216911419828)
y = 4758.25367129741
y = 4758.25
Don't forget to round to the nearest cent.
Use a net to find the surface area of the cereal box
Answers
Answer:
206
Step-by-step explanation:
A=2(wl+hl+hw)
Ben's living room is a rectangle measuring 12 yards by 144 inches. By how many feet does the length of the room exceed the width? PLEASE ANSWER PLEASE
Answers
Answer:
24 feet
Step-by-step explanation:
ok, so first we need convert the yards into feet.
12 yards=36 feet
(one yard=3 feet)
then, we need to convert the inches into feet.
144 inches=12 feet
(one foot=12 inches)
so now, our dimensions are 36 feet by 12 feet
36-12=24
the length of the room exceeds the width by 24 feet!
hope this helped <33333333333
32 is 32% of what?????
Answers
Answer:
32 is 32% of 100
Step-by-step explanation:
Answer: 100
Step-by-step explanation: 32 is 32% of 100
Mary split her gross pay from last week equally between her student loans, rent, and savings. She put $450 in her savings account. Write and solve an equation to determine how much Mary earned last week.
Answers
Answer:
1350
Step-by-step explanation:
if she spilt her pay EQUALLY between 3 things, and she added 450 to her savings, everything else would be 450 too. so 450 x 3 = 1350
i will give Brainiest if you are right
Answers
Answer:
19.5º
Step-by-step explanation:
Every triangle is equal to 180º for all angles. So, you add 33.5 + 127 and subtract the sum by 180.
33.5 + 127= 160.5
180- 160.5 = 19.5
So, the angle F is 19.5º
Hope this helps !!
-Ketifa
Answer:
look at the picture I sent
Please help! Ubehebe crater in death Valley has a diameter of a little more than 1/2 a mile. If Latisha walks around its rim at a rate of 2 mph, about how long will it take her to walk all the way around the crater? Round your answer to the nearest tenth. Use 3.14 for pi.
Answers
The time required for Latisha to walk around the rim at a rate of 2 mph is 0.235 hours.
What is speed?Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.
here,
Ubehebe crater in Death Valley has a diameter of a little more than 1/2 a mile.
Circumference of the rim,
= πD
= 3.14 × 1/2
= 1.57 mile
Time = Distance/speed
Time = 1.57 / 2
Time = 0.785 hours
Thus, the time required for Latisha to walk around the rim at a rate of 2 mph is 0.235 hours.
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solve the equation a^2x^2 = abx + 2b^2 using completing the square method
Answers
The solution to the equation is
x = b/a ± √(b^2/a^2) / a.
What is the equation?Generally, To solve the equation using the completing the square method, we first move all the terms to one side of the equation by subtracting abx and 2b² from both sides, giving us:
a²x² = abx + 2b²
Which is
a²x² - abx - 2b² = 0
Next, we need to add and subtract a term so that the left side of the equation can be written as a perfect square.
We need to find the square of half of the coefficient of the x term, which is -ab/2a.
So we add and subtract (ab/2a)^2 = (b^2/a^2) on the left side of the equation:
a²x² - abx - 2b² + (b²/a²) - (b²/a²) = 0
This gives us the left side of the equation as
(ax - b/a)² = b²/a².
We can then take the square root of both sides:
ax - b/a = ±√(b²/a²)
Finally, we can add b/a to both sides to get the solution:
x = b/a ± √(b²/a²) / a
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Lupe wrote two different fractions with the same denominator. both fractions were less than 1. can their sum equal? can their sum be greater than 1?
Answers
Answer: it depends on the number you took
Step-by-step explanation: