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)

Expressing 15^(x) in A^((x)/(6)) form: We need to express 15^(x) in the form of A^((x)/(6)). To do this, we need to find a base A such that when raised to the power of (x/6), it is equivalent to 15^(x).Equating the exponents: Let's assume 15^(x) = A^((x)/(6)). To find A, we need to equate the exponents of both sides. Since the exponent on the right side is (x/6), 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: (A) A=15^(-6) is incorrect because it represents the reciprocal of the sixth power of 15, not the sixth root. (B) A=15^(6) is incorrect because it represents the sixth power of 15, not the sixth root. (C) A=15^(-(1)/(6)) is incorrect because it represents the reciprocal of the sixth root of 15. (D) A=15^(1/6) is correct because it represents the sixth root of 15, which is what we need for A.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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) $A=\frac{15}{6}$

View step-by-step help

Home

Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. What is the value of

A

when we rewrite

15^{x}

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 $A$ .