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Select all the expressions that are equivalent to $8^3 \times 8^4$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{8^{-7}}$ $\newline$ (B) $\frac{1}{8^7}$ $\newline$ (C) $8^7$ $\newline$ (D) $\frac{1}{8^{12}}$

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Divide numbers written in scientific notation

Full solution

Q. Select all the expressions that are equivalent to

8^3 \times 8^4

.

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{8^{-7}}

\newline

(B)

\frac{1}{8^7}

\newline

(C)

8^7

\newline

(D)

\frac{1}{8^{12}}

Apply Exponent Rule: Apply the rule of exponents for multiplication. $\newline$ When multiplying powers with the same base, you add the exponents. $\newline$ $8^3 \times 8^4 = 8^{(3 + 4)} = 8^7$
Compare with Choices: Compare the result from Step $1$ with each of the given choices. $\newline$ (A) $\frac{1}{8^{-7}}$ is equivalent to $8^7$ because the negative exponent means the reciprocal. $\newline$ (B) $\frac{1}{8^7}$ is not equivalent to $8^7$ because it is the reciprocal of $8^7$ . $\newline$ (C) $8^7$ is equivalent to $8^7$ , which is the result we obtained in Step $1$ . $\newline$ (D) $\frac{1}{8^{12}}$ is not equivalent to $8^7$ because it is the reciprocal of $8^{12}$ , not $8^7$ .

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