Which expression is equivalent to (4^4)^8? Choices: (A)1/4^12 (B)4^32 (C)4^12 (D)1/4^32

Understand Exponent Rule: Understand the exponent rule for powers raised to powers. When a power is raised to another power, we multiply the exponents. (a^m)^n = a^(m*n)Apply Rule to Expression: Apply the exponent rule to the given expression (4^4)^8. Multiply the exponents 4 and 8. (4^4)^8 = 4^(4*8) = 4^32Compare with Choices: Compare the result with the given choices. The expression 4^32 matches choice (B).

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Which expression is equivalent to $(4^4)^8$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{4^{12}}$ $\newline$ (B) $4^{32}$ $\newline$ (C) $4^{12}$ $\newline$ (D) $\frac{1}{4^{32}}$

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Math Problems

Algebra 1

Identify equivalent exponential expressions II

Full solution

Q. Which expression is equivalent to

(4^4)^8

\newline

Choices:

\newline

(A)

\frac{1}{4^{12}}

\newline

(B)

4^{32}

\newline

(C)

4^{12}

\newline

(D)

\frac{1}{4^{32}}

Understand Exponent Rule: Understand the exponent rule for powers raised to powers. $\newline$ When a power is raised to another power, we multiply the exponents. $\newline$ $(a^m)^n = a^{(m*n)}$
Apply Rule to Expression: Apply the exponent rule to the given expression $(4^4)^8$ . Multiply the exponents $4$ and $8$ . $(4^4)^8 = 4^{(4*8)} = 4^{32}$
Compare with Choices: Compare the result with the given choices. $\newline$ The expression $4^{32}$ matches choice (B).