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2 years ago

Simplify (2^5/3^2)^4

Mathematics

1 answer:

Debora [2.8K]2 years ago

8 0

Answer:

( 2^(20) / 3^(8) )

Step-by-step explanation:

(2^5/3^2)^4

=>( 2^(5(4)) / 3^(2(4)) )

=> ( 2^(20) / 3^(8) )

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Which could be the first step in simplifying this expression? Check all that apply. (x cubed x Superscript negative 6 Baseline)

PtichkaEL [24]

Answer:

$(x^{-3} )^{2}$

$x^6 x^{-12}$

Step-by-step explanation:

$(x^{3} x^{-6} )^{2}$ is the expression given to be solved.

First of all let us have a look at 3 formulas:

$1.\ p^a \times p^b = p^{(a+b)}\\2.\ (p^a \times q^b)^c = (p^{a})^c \times (q^{b})^c\\3.\ (p^a)^b = p^{a\times b}$

Both the formula can be applied to the expression( $(x^{3} x^{-6} )^{2}$ ) during the first step while solving it.

Applying formula (1):

$(x^{3} x^{-6} )^{2}$

Comparing the terms of $(x^{3} x^{-6} )$ with $p^a \times p^b$

$p=x, a =3, b=-6$

$\Rightarrow x^{3+(-6)}\\\Rightarrow x^{3-6}\\\Rightarrow x^{-3}$

So, $(x^{3} x^{-6} )^{2}$ is reduced to $(x^{-3} )^{2}$

Applying formula (2):

Comparing the terms of $(x^{3} x^{-6} )^{2}$ with $(p^a \times q^b)^c$

$p=q=x, a =3, b=-6, c=2$

$\Rightarrow (x^{3})^2\times (x^{-6})^2\\\text{Applying Formula (3)}\\x^6 x^{-12}$

So, $(x^{3} x^{-6} )^{2}$ is reduced to $x^6 x^{-12}$ .

So, the answers can be:

$(x^{-3} )^{2}$

$x^6 x^{-12}$

8 0

2 years ago

1. Complete the inequality below to describe the

dezoksy [38]

Domain is the entire span left to right (on the x-axis) that the graph is on. Since the graph goes from x=-4 and ends at x=4, the domain would be from -4 to 4. The circle at -4 is open, so it does not include the point at -4, just everything leading up to it. So, the domain would be

$- 4 < x \leqslant 4$

The range is similar, it is the entire span that the graph goes up and down (on the y-axis). The graph starts at the bottom at y=-2, and ends at y=5. The bottom point (4,-2) is closed, so the graph includes that point, and the top point (-4,5) is open and doesn't include the point. Therefore, the range would be

$- 2 \leqslant x < 5$

5 0

2 years ago

Read 2 more answers

Laura rents a movie for a flat fee of $2.00 plus an additional $0.50 for each night she keeps the movie. Choose the cost functio

daser333 [38]

Answer:

The cost function that represents this scenario is c(x) = 2 + 0.50x .

Option (b) is correct .

Step-by-step explanation:

As given

Laura rents a movie for a flat fee of $2.00 plus an additional $0.50 for each night she keeps the movie.

if x equals the number of nights Laura has the movie.

Than the cost function that represents this scenario .

c(x) = Flat fee + Cost for x equals the number of nights Laura has the movie.

c(x) = 2 + x × 0.50

c(x) = 2 + 0.50x

Therefore the cost function that represents this scenario is c (x) = 2 + 0.50x .

Option (b) is correct .

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3 years ago

Read 2 more answers

Which of the following are equivalent to the expression x^1/3*x^1/2? Select all that apply

mars1129 [50]

Answer:

options 2,4 and 6 should be correct.

Step-by-step explanation:

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3 years ago

How many 2cm×2cm cubes can be packed in a box 1m long,20cm wide and 4cm deep.

Artemon [7]

Answer:

yetrygegegegr

Step-by-step explanation:

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2 years ago