Select all the expressions that are equivalent to 7^-2 * 4^-2. Multi-select Choices: (A)1/28^-2 (B)28^-2 (C)1/28^2 (D)28^4

Simplify Expression: Step 1: Simplify the expression 7^-2 * 4^-2. Calculation: 7^-2 means 1/7^2 and 4^-2 means 1/4^2. So, 7^-2 * 4^-2 = (1/7^2) * (1/4^2) = 1/(7^2 * 4^2) = 1/49 * 16 = 1/784.Compare with Choices: Step 2: Compare the simplified expression with the choices. Calculation: 1/784 needs to be compared with each choice. (A) 1/28^-2 = 1/(1/28^2) = 28^2 = 784, not 1/784. (B) 28^-2 = 1/28^2 = 1/784, this matches. (C) 1/28^2 = 1/784, this also matches. (D) 28^4 = 614656, not 1/784.

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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

7^{-2} \times 4^{-2}

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Multi-select Choices:

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(A)

\frac{1}{28^{-2}}

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(B)

28^{-2}

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(C)

\frac{1}{28^{2}}

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(D)

28^{4}

Simplify Expression: Step $1$ : Simplify the expression $7^{-2} \times 4^{-2}$ . $\newline$ Calculation: $7^{-2}$ means $1/7^2$ and $4^{-2}$ means $1/4^2$ . $\newline$ So, $7^{-2} \times 4^{-2} = (1/7^2) \times (1/4^2) = 1/(7^2 \times 4^2) = 1/49 \times 16 = 1/784$ .
Compare with Choices: Step $2$ : Compare the simplified expression with the choices. $\newline$ Calculation: $1/784$ needs to be compared with each choice. $\newline$ (A) $1/28^{-2} = 1/(1/28^2) = 28^2 = 784$ , not $1/784$ . $\newline$ (B) $28^{-2} = 1/28^2 = 1/784$ , this matches. $\newline$ (C) $1/28^2 = 1/784$ , this also matches. $\newline$ (D) $28^4 = 614656$ , not $1/784$ .