Select all the expressions that are equivalent to 3^-8 * 3^-3. Multi-select Choices: (A)3^-11 (B)3^24 (C)3^-8/3^3 (D)1/3^-11

Calculate Exponents: Step 1: Calculate the product of 3^-8 and 3^-3. When multiplying powers with the same base, add the exponents. 3^-8 * 3^-3 = 3^(-8 + (-3)) = 3^-11 Compare with Choices: Step 2: Compare the result with the given choices. (A) 3^-11 matches our calculation. (B) 3^24 is not equivalent because it has a positive exponent and is a product, not a quotient. (C) 3^-8/3^3 simplifies to 3^-11, which matches our calculation. (D) 1/3^-11 simplifies to 3^11, which is not equivalent because it has a positive exponent.

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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

3^{-8} \times 3^{-3}

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Multi-select Choices:

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(A)

3^{-11}

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(B)

3^{24}

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(C)

\frac{3^{-8}}{3^{3}}

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(D)

\frac{1}{3^{-11}}

Calculate Exponents: Step $1$ : Calculate the product of $3^{-8}$ and $3^{-3}$ . $\newline$ When multiplying powers with the same base, add the exponents. $\newline$ $3^{-8} \times 3^{-3} = 3^{(-8 + (-3))} = 3^{-11}$
Compare with Choices: Step $2$ : Compare the result with the given choices. $\newline$ (A) $3^{-11}$ matches our calculation. $\newline$ (B) $3^{24}$ is not equivalent because it has a positive exponent and is a product, not a quotient. $\newline$ (C) $\frac{3^{-8}}{3^{3}}$ simplifies to $3^{-11}$ , which matches our calculation. $\newline$ (D) $\frac{1}{3^{-11}}$ simplifies to $3^{11}$ , which is not equivalent because it has a positive exponent.