Select all the expressions that are equivalent to 7^-3 * 7^-3. Multi-select Choices: (A)1/7^-6 (B)7^-6 (C)1/7^6 (D)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 * 7^-3 = 7^(-3 + -3) = 7^-6 Compare with choices: Step 2: Compare the result with the given choices. We have 7^-6 from our calculation. Now, let's match it with the choices: (A) 1/7^-6 is equivalent to 7^6, which is not the same as 7^-6. (B) 7^-6 matches exactly with our result. (C) 1/7^6 is the reciprocal of 7^6, which is not the same as 7^-6. (D) 1/7^9 is the reciprocal of 7^9, which is also not the same as 7^-6.

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Math Problems

Algebra 1

Simplify exponential expressions using exponent rules

Full solution

Q. Select all the expressions that are equivalent to

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

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Multi-select Choices:

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(A)

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

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(B)

7^{-6}

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(C)

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

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(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 $7^{-6}$ .