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

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

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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

12^7 \times 12^{-5}

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Multi-select Choices:

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(A)

12^2

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(B)

1/12^{-35}

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(C)

1/12^{-2}

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(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 $2$ .