Which exponential expression is equivalent to (root(7)(a))^(2) ? Choose 1 answer: (A) a^((7)/(2)) (B) a^((2)/(7)) (C) (a^(7))/(a^(2)) (D) (a^(2))/(a^(7))

Problem Understanding: Let's first understand the problem. We need to find an equivalent exponential expression for (root(7)(a))^2.Rewriting the Expression: The 7th root of a can be written as a^(1/7). So, (root(7)(a))^2 can be rewritten as (a^(1/7))^2.Simplifying the Expression: Using the power of a power rule, which states that (a^m)^n = a^(m*n), we can simplify (a^(1/7))^2 to a^((1/7)*2).Calculating the Exponent: Now, we calculate (1/7)*2 which equals 2/7. So, (a^(1/7))^2 simplifies to a^(2/7).Matching the Result: Comparing our result with the given choices, we find that a^(2/7) matches choice (B) a^((2)/(7)).

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Which exponential expression is equivalent to
(root(7)(a))^(2) ?
Choose 1 answer:
(A)
a^((7)/(2))
(B)
a^((2)/(7))
(C)
(a^(7))/(a^(2))
(D)
(a^(2))/(a^(7))

Which exponential expression is equivalent to $(\sqrt[7]{a})^{2}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $a^{\frac{7}{2}}$ $\newline$ (B) $a^{\frac{2}{7}}$ $\newline$ (C) $\frac{a^{7}}{a^{2}}$ $\newline$ (D) $\frac{a^{2}}{a^{7}}$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. Which exponential expression is equivalent to

(\sqrt[7]{a})^{2}

\newline

Choose

1

answer:

\newline

(A)

a^{\frac{7}{2}}

\newline

(B)

a^{\frac{2}{7}}

\newline

(C)

\frac{a^{7}}{a^{2}}

\newline

(D)

\frac{a^{2}}{a^{7}}

Problem Understanding: Let's first understand the problem. We need to find an equivalent exponential expression for $(\sqrt[7]{a})^2$ .
Rewriting the Expression: The $7$ th root of $a$ can be written as $a^{(1/7)}$ . So, $(\sqrt[7]{a})^2$ can be rewritten as $(a^{(1/7)})^2$ .
Simplifying the Expression: Using the power of a power rule, which states that $(a^m)^n = a^{(m*n)}$ , we can simplify $(a^{(1/7)})^2$ to $a^{((1/7)*2)}$ .
Calculating the Exponent: Now, we calculate $(\frac{1}{7})\cdot 2$ which equals $\frac{2}{7}$ . So, $(a^{\frac{1}{7}})^2$ simplifies to $a^{\frac{2}{7}}$ .
Matching the Result: Comparing our result with the given choices, we find that $a^{\frac{2}{7}}$ matches choice (B) $a^{\left(\frac{2}{7}\right)}$ .