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Select all the expressions that are equivalent to $12^7 \times 12^{-5}$ . $\newline$ Multi-select Choices: $\newline$ (A) $12^2$ $\newline$ (B) $1/12^{-35}$ $\newline$ (C) $1/12^{-2}$ $\newline$ (D) $12^{-35}$

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Simplify exponential expressions using exponent rules

Full solution

Q. Select all the expressions that are equivalent to

12^7 \times 12^{-5}

.

\newline

Multi-select Choices:

\newline

(A)

12^2

\newline

(B)

1/12^{-35}

\newline

(C)

1/12^{-2}

\newline

(D)

12^{-35}

Simplify Expression: Simplify the expression $12^7 \times 12^{-5}$ . When multiplying powers with the same base, we add the exponents. $12^7 \times 12^{-5} = 12^{7 + (-5)} = 12^2$
Add Exponents: Compare the simplified expression to the choices. $\newline$ The simplified expression is $12^2$ . Let's see which choices match this expression. $\newline$ (A) $12^2$ is clearly the same as our simplified expression. $\newline$ (B) $\frac{1}{12^{-35}}$ is not equivalent because the exponent is $-35$ , not $2$ . $\newline$ (C) $\frac{1}{12^{-2}}$ is equivalent because the negative exponent in the denominator means the base is actually in the numerator with a positive exponent: $\frac{1}{12^{-2}} = 12^2$ . $\newline$ (D) $12^{-35}$ is not equivalent because the exponent is $-35$ , not $2$ .

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