Which expression is equivalent to 5^4 * 5^8? Choices: (A)1/5^32 (B)5^32 (C)5^12 (D)1/5^12

Identify Operation: Identify the operation to perform with the exponents. When we multiply powers with the same base, we add the exponents. a^m * a^n = a^(m+n)Add Exponents: Add the exponents of the powers of 5. 5^4 * 5^8 = 5^(4+8) Calculate the sum of the exponents. 5^(4+8) = 5^12Calculate Sum: Match the result with the given choices. The expression 5^12 corresponds to choice (C) 5^12.

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Which expression is equivalent to $5^4 \times 5^8$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{5^{32}}$ $\newline$ (B) $5^{32}$ $\newline$ (C) $5^{12}$ $\newline$ (D) $\frac{1}{5^{12}}$

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Math Problems

Algebra 1

Identify equivalent exponential expressions II

Full solution

Q. Which expression is equivalent to

5^4 \times 5^8

\newline

Choices:

\newline

(A)

\frac{1}{5^{32}}

\newline

(B)

5^{32}

\newline

(C)

5^{12}

\newline

(D)

\frac{1}{5^{12}}

Identify Operation: Identify the operation to perform with the exponents. $\newline$ When we multiply powers with the same base, we add the exponents. $\newline$ $a^m \times a^n = a^{(m+n)}$
Add Exponents: Add the exponents of the powers of $5$ . $\newline$ $5^4 \times 5^8 = 5^{4+8}$ $\newline$ Calculate the sum of the exponents. $\newline$ $5^{4+8} = 5^{12}$
Calculate Sum: Match the result with the given choices. $\newline$ The expression $5^{12}$ corresponds to choice (C) $5^{12}$ .