Which expression is equivalent to 5^9 * 5^7? Choices: (A)5^63 (B)1/5^63 (C)5^16 (D)1/5^16

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. 5^9 * 5^7 = 5^(9+7) = 5^16Match Result: Match the result with the given choices. The expression 5^16 corresponds to choice (C).

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Which expression is equivalent to $5^9 \times 5^7$ ? $\newline$ Choices: $\newline$ (A) $5^{63}$ $\newline$ (B) $\frac{1}{5^{63}}$ $\newline$ (C) $5^{16}$ $\newline$ (D) $\frac{1}{5^{16}}$

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Math Problems

Algebra 1

Identify equivalent exponential expressions II

Full solution

Q. Which expression is equivalent to

5^9 \times 5^7

\newline

Choices:

\newline

(A)

5^{63}

\newline

(B)

\frac{1}{5^{63}}

\newline

(C)

5^{16}

\newline

(D)

\frac{1}{5^{16}}

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 $5$ . $5^9 \times 5^7$ $= 5^{(9+7)}$ $= 5^{16}$
Match Result: Match the result with the given choices. $\newline$ The expression $5^{16}$ corresponds to choice (C).