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What is the value of
A when we rewrite
15^(x) as
A^((x)/(6)) ?
Choose 1 answer:
(A)
A=15^(-6)
(B)
A=15^(6)
(C)
A=15^(-(1)/(6))
(D)
A=(15)/(6)

What is the value of $A$ when we rewrite $15^{x}$ as $A^{\frac{x}{6}}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $A=15^{-6}$ $\newline$ (B) $A=15^{6}$ $\newline$ (C) $A=15^{-\frac{1}{6}}$ $\newline$ (D) $A=\frac{15}{6}$

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Compare linear and exponential growth

Full solution

Q. What is the value of

A

when we rewrite

15^{x}

as

A^{\frac{x}{6}}

?

\newline

Choose

1

answer:

\newline

(A)

A=15^{-6}

\newline

(B)

A=15^{6}

\newline

(C)

A=15^{-\frac{1}{6}}

\newline

(D)

A=\frac{15}{6}

Expressing $15^{x}$ in $A^{\left(\frac{x}{6}\right)}$ form: We need to express $15^{x}$ in the form of $A^{\left(\frac{x}{6}\right)}$ . To do this, we need to find a base $A$ such that when raised to the power of $\left(\frac{x}{6}\right)$ , it is equivalent to $15^{x}$ .
Equating the exponents: Let's assume $15^{x} = A^{\left(\frac{x}{6}\right)}$ . To find $A$ , we need to equate the exponents of both sides. Since the exponent on the right side is $\left(\frac{x}{6}\right)$ , we need to find the sixth root of $15$ to make the bases equal.
Finding the base $A$ : Taking the sixth root of $15$ is the same as raising $15$ to the power of $1/6$ . Therefore, $A$ should be equal to $15^{1/6}$ .
Comparing the options: Now we compare the options given to find which one matches our result: $\newline$ (A) $A=15^{-6}$ is incorrect because it represents the reciprocal of the sixth power of $15$ , not the sixth root. $\newline$ (B) $A=15^{6}$ is incorrect because it represents the sixth power of $15$ , not the sixth root. $\newline$ (C) $A=15^{-\left(\frac{1}{6}\right)}$ is incorrect because it represents the reciprocal of the sixth root of $15$ . $\newline$ (D) $A=15^{\frac{1}{6}}$ is correct because it represents the sixth root of $15$ , which is what we need for $A$ .

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\newline

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f(x)

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\newline

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\newline

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\newline

Simplify any fractions.

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are differentiable.

\newline

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\newline

Simplify any fractions.

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u(x)

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\newline

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\newline

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\newline

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\newline

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\newline

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