Select all the expressions that are equivalent to (5^4)^2. Multi-select Choices: (A)1/5^8 (B)5^6 (C)5^8 (D)1/5^6

Apply Power Rule: Apply the power of a power rule for exponents, which states that (a^m)^n = a^(m*n). Calculate (5^4)^2 using the power of a power rule. (5^4)^2 = 5^(4*2) = 5^8Calculate (5^4)^2: Compare the result from Step 1 with the given choices to determine which expressions are equivalent. (A) 1/5^8 is not equivalent because it represents the reciprocal of 5^8. (B) 5^6 is not equivalent because the exponent is 6, not 8. (C) 5^8 is equivalent because it matches the result from Step 1. (D) 1/5^6 is not equivalent because it represents the reciprocal of 5^6 and the exponent is 6, not 8.

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Select all the expressions that are equivalent to $(5^4)^2$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{5^8}$ $\newline$ (B) $5^6$ $\newline$ (C) $5^8$ $\newline$ (D) $\frac{1}{5^6}$

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Math Problems

Algebra 2

Simplify rational expressions

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Q. Select all the expressions that are equivalent to

(5^4)^2

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{5^8}

\newline

(B)

5^6

\newline

(C)

5^8

\newline

(D)

\frac{1}{5^6}

Apply Power Rule: Apply the power of a power rule for exponents, which states that a^m)^n = a^{m*n}\.\(\newlineCalculate \(5^ $4$ )^ $2$ \ using the power of a power rule. $\newline$ \(5^ $4$ )^ $2$ = $5$ ^{ $4$ * $2$ } = $5$ ^ $8$ \
Calculate $(5^4)^2$ : Compare the result from Step $1$ with the given choices to determine which expressions are equivalent. $\newline$ (A) $\frac{1}{5^8}$ is not equivalent because it represents the reciprocal of $5^8$ . $\newline$ (B) $5^6$ is not equivalent because the exponent is $6$ , not $8$ . $\newline$ (C) $5^8$ is equivalent because it matches the result from Step $1$ . $\newline$ (D) $\frac{1}{5^6}$ is not equivalent because it represents the reciprocal of $5^6$ and the exponent is $6$ , not $8$ .