What is the value of A when we rewrite ((7)/(3))^(x) as A^(2x) ? Choose 1 answer: (A) A=(1)/(2) (B) A=((7)/(3))^((1)/(2)) (c) A=((7)/(3))^(-2) (D) A=(3)/(7)

Given expression: We are given the expression ((7)/(3))^(x) and we want to rewrite it in the form A^(2x). To do this, we need to find a base A such that A^(2x) is equivalent to ((7)/(3))^(x).Equating the expressions: To find A, we need to equate the two expressions: ((7)/(3))^(x) = A^(2x) Since the exponents must be the same for the bases to be equal, we can rewrite the right side to have the same exponent as the left side by taking the square root of A: ((7)/(3))^(x) = (A^2)^(x)Finding A: Now we can equate the bases: (7/3) = A^2 To find A, we take the square root of both sides: A = sqrt(7/3)Simplifying the square root: Simplifying the square root of the fraction, we get: A = ((7)/(3))^((1)/(2)) This matches one of the given answer choices.

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What is the value of
A when we rewrite
((7)/(3))^(x) as
A^(2x) ?
Choose 1 answer:
(A)
A=(1)/(2)
(B)
A=((7)/(3))^((1)/(2))
(c)
A=((7)/(3))^(-2)
(D)
A=(3)/(7)

What is the value of $A$ when we rewrite $\left(\frac{7}{3}\right)^{x}$ as $A^{2 x}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $A=\frac{1}{2}$ $\newline$ (B) $A=\left(\frac{7}{3}\right)^{\frac{1}{2}}$ $\newline$ (C) $A=\left(\frac{7}{3}\right)^{-2}$ $\newline$ (D) $A=\frac{3}{7}$

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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{7}{3}\right)^{x}

A^{2 x}

\newline

Choose

1

answer:

\newline

(A)

A=\frac{1}{2}

\newline

(B)

A=\left(\frac{7}{3}\right)^{\frac{1}{2}}

\newline

(C)

A=\left(\frac{7}{3}\right)^{-2}

\newline

(D)

A=\frac{3}{7}

Given expression: We are given the expression $\left(\frac{7}{3}\right)^{x}$ and we want to rewrite it in the form $A^{2x}$ . To do this, we need to find a base $A$ such that $A^{2x}$ is equivalent to $\left(\frac{7}{3}\right)^{x}$ .
Equating the expressions: To find $A$ , we need to equate the two expressions: $\newline$ $\left(\frac{7}{3}\right)^{x} = A^{2x}$ $\newline$ Since the exponents must be the same for the bases to be equal, we can rewrite the right side to have the same exponent as the left side by taking the square root of $A$ : $\newline$ $\left(\frac{7}{3}\right)^{x} = (A^2)^{x}$
Finding A: Now we can equate the bases: $\newline$ $(\frac{7}{3}) = A^2$ $\newline$ To find A, we take the square root of both sides: $\newline$ $A = \sqrt{\frac{7}{3}}$
Simplifying the square root: Simplifying the square root of the fraction, we get: $\newline$ $A = \left(\frac{7}{3}\right)^{\frac{1}{2}}$ $\newline$ This matches one of the given answer choices.