Select all the expressions that are equivalent to 8^7 * 8^6. Multi-select Choices: (A)1/8^13 (B)1/8^42 (C)8^42 (D)1/8^-13

Apply Exponent Rule: Use the property of exponents that states when you multiply powers with the same base, you add the exponents. So, $8^7 \cdot 8^6 = 8^{7+6}$.Add Exponents: Perform the addition of the exponents. $8^{7+6} = 8^{13}$.Compare with Choices: Compare the result with the given choices to determine which expressions are equivalent to $8^{13}$. (A) $1/8^{13}$ is the reciprocal of $8^{13}$, not equivalent. (B) $1/8^{42}$ is the reciprocal of $8^{42}$, not equivalent and the exponent is incorrect. (C) $8^{42}$ has a much larger exponent than $8^{13}$, not equivalent. (D) $1/8^{-13}$ is the reciprocal of $8^{-13}$, which is equivalent to $8^{13}$ because $1/a^{-n} = a^n$.

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Select all the expressions that are equivalent to $8^7 \times 8^6$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{8^{13}}$ $\newline$ (B) $\frac{1}{8^{42}}$ $\newline$ (C) $8^{42}$ $\newline$ (D) $\frac{1}{8^{-13}}$

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Math Problems

Algebra 2

Simplify rational expressions

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Q. Select all the expressions that are equivalent to

8^7 \times 8^6

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{8^{13}}

\newline

(B)

\frac{1}{8^{42}}

\newline

(C)

8^{42}

\newline

(D)

\frac{1}{8^{-13}}

Apply Exponent Rule: Use the property of exponents that states when you multiply powers with the same base, you add the exponents. $\newline$ So, $8^7 \cdot 8^6 = 8^{7+6}$ .
Add Exponents: Perform the addition of the exponents. $\newline$ $8^{7+6} = 8^{13}$ .
Compare with Choices: Compare the result with the given choices to determine which expressions are equivalent to $8^{13}$ . $\newline$ (A) $1/8^{13}$ is the reciprocal of $8^{13}$ , not equivalent. $\newline$ (B) $1/8^{42}$ is the reciprocal of $8^{42}$ , not equivalent and the exponent is incorrect. $\newline$ (C) $8^{42}$ has a much larger exponent than $8^{13}$ , not equivalent. $\newline$ (D) $1/8^{-13}$ is the reciprocal of $8^{-13}$ , which is equivalent to $8^{13}$ because $1/8^{13}$ $0$ .