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Select all the expressions that are equivalent to $7^{-3} \times 7^{-3}$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{7^{-6}}$ $\newline$ (B) $7^{-6}$ $\newline$ (C) $\frac{1}{7^{6}}$ $\newline$ (D) $\frac{1}{7^{9}}$

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Simplify exponential expressions using exponent rules

Full solution

Q. Select all the expressions that are equivalent to

7^{-3} \times 7^{-3}

.

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{7^{-6}}

\newline

(B)

7^{-6}

\newline

(C)

\frac{1}{7^{6}}

\newline

(D)

\frac{1}{7^{9}}

Calculate product: Step $1$ : Calculate the product of $7^{-3}$ and $7^{-3}$ . We know that when multiplying powers with the same base, we add the exponents. $7^{-3} \times 7^{-3} = 7^{(-3 + -3)} = 7^{-6}$
Compare with choices: Step $2$ : Compare the result with the given choices. $\newline$ We have $7^{-6}$ from our calculation. Now, let's match it with the choices: $\newline$ (A) $1/7^{-6}$ is equivalent to $7^6$ , which is not the same as $7^{-6}$ . $\newline$ (B) $7^{-6}$ matches exactly with our result. $\newline$ (C) $1/7^6$ is the reciprocal of $7^6$ , which is not the same as $7^{-6}$ . $\newline$ (D) $1/7^9$ is the reciprocal of $7^9$ , which is also not the same as $7^{-6}$ .

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