What is the value of A when we rewrite ((32)/(5))^(-2x) as A^(x) ? Choose 1 answer: (A) A=-(64)/(5) (B) A=(1)/(2) (c) A=((5)/(32))^(-2) (D) A=((32)/(5))^(-2)

Identify Base A: We need to express ((32)/(5))^(-2x) in the form of A^(x). To do this, we will find a base A such that A^(x) is equivalent to ((32)/(5))^(-2x).Focus on (32/5): First, let's focus on the base of the exponent, which is (32/5). We want to find A such that A^(x) = ((32)/(5))^(-2x). To do this, we need to find a base that, when raised to the power of x, gives the same result as (32/5) raised to the power of -2x.Rewrite as (32/5)^(-2): We can rewrite ((32)/(5))^(-2x) as ((32)/(5))^(-2))^x by using the property of exponents that states (b^(m))^n = b^(mn). This means we are looking for A such that A = ((32)/(5))^(-2).Calculate (32/5)^(-2): Now, let's calculate ((32)/(5))^(-2). This is the same as (5/32)^2 because a negative exponent indicates reciprocal, and then we square the result.Compare with Answer Choices: Calculating (5/32)^2 gives us (5^2)/(32^2) = 25/1024. This is the value of A.Now we compare the value of A we found with the answer choices. The value of A is 25/1024, which is not listed in the answer choices directly. However, we can see that this is equivalent to ((5)/(32))^2, which is the reciprocal of the base raised to the power of -2. Therefore, the correct answer choice is (C) A=((5)/(32))^(-2).

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What is the value of
A when we rewrite
((32)/(5))^(-2x) as
A^(x) ?
Choose 1 answer:
(A)
A=-(64)/(5)
(B)
A=(1)/(2)
(c)
A=((5)/(32))^(-2)
(D)
A=((32)/(5))^(-2)

What is the value of $A$ when we rewrite $\left(\frac{32}{5}\right)^{-2 x}$ as $A^{x}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $A=-\frac{64}{5}$ $\newline$ B $A=\frac{1}{2}$ $\newline$ (C) $A=\left(\frac{5}{32}\right)^{-2}$ $\newline$ (D) $A=\left(\frac{32}{5}\right)^{-2}$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. What is the value of

A

when we rewrite

\left(\frac{32}{5}\right)^{-2 x}

A^{x}

\newline

Choose

1

answer:

\newline

(A)

A=-\frac{64}{5}

\newline

A=\frac{1}{2}

\newline

(C)

A=\left(\frac{5}{32}\right)^{-2}

\newline

(D)

A=\left(\frac{32}{5}\right)^{-2}

Identify Base A: We need to express $\left(\frac{32}{5}\right)^{-2x}$ in the form of $A^{x}$ . To do this, we will find a base $A$ such that $A^{x}$ is equivalent to $\left(\frac{32}{5}\right)^{-2x}$ .
Focus on $(\frac{32}{5}):</b> First, let's focus on the base of the exponent, which is \$(\frac{32}{5})$ . We want to find $A$ such that $A^{x} = (\frac{32}{5})^{-2x}$ . To do this, we need to find a base that, when raised to the power of $x$ , gives the same result as $(\frac{32}{5})$ raised to the power of $-2x$ .
Rewrite as $(32/5)^{-2}$ : We can rewrite $\left(\frac{32}{5}\right)^{-2x}$ as $\left(\frac{32}{5}\right)^{-2}$ ^x by using the property of exponents that states $(b^{m})^{n} = b^{mn}$ . This means we are looking for $A$ such that $A = \left(\frac{32}{5}\right)^{-2}$ .
Calculate $(32/5)^{-2}$ : Now, let's calculate $((32)/(5))^{-2}$ . This is the same as $(5/32)^2$ because a negative exponent indicates reciprocal, and then we square the result.
Compare with Answer Choices: Calculating $(\frac{5}{32})^2$ gives us $(5^2)/(32^2) = \frac{25}{1024}$ . This is the value of $A$ .
Compare with Answer Choices: Calculating $(5/32)^2$ gives us $(5^2)/(32^2) = 25/1024$ . This is the value of $A$ .Now we compare the value of $A$ we found with the answer choices. The value of $A$ is $25/1024$ , which is not listed in the answer choices directly. However, we can see that this is equivalent to $((5)/(32))^2$ , which is the reciprocal of the base raised to the power of $-2$ . Therefore, the correct answer choice is $(C) A=((5)/(32))^(-2)$ .

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