Which expressions are equivalent to 4^(-2)*7^(-2) ? Choose 2 answers: (A) (4*7)^(-4) (B) (1)/(28^(2)) (C) (7^(-2))/(4^(2)) (D) (4*7)^(4)

Understand Given Expression: Understand the given expression. We are given the expression 4^(-2)*7^(-2) and we need to find which of the provided options are equivalent to this expression.Simplify Using Exponents: Simplify the given expression using the property of exponents. When we multiply two exponents with the same negative exponent, we can combine the bases and keep the exponent. 4^(-2)*7^(-2) = (4*7)^(-2)Check Option A: Check option A: (4*7)^(-4) This option has a different exponent than what we derived in Step 2. Therefore, option A is not equivalent to the given expression.Check Option B: Check option B: (1)/(28^(2)) Rewrite the simplified expression from Step 2 as a fraction. (4*7)^(-2) = 1/(4*7)^(2) = 1/(28^(2)) Option B is equivalent to the given expression.Check Option C: Check option C: (7^(-2))/(4^(2)) This option does not match the simplified expression from Step 2 because the exponents are not the same for both the numerator and the denominator. Therefore, option C is not equivalent to the given expression.Check Option D: Check option D: (4*7)^(4) This option has a positive exponent and is raised to the power of 4, which is different from the negative exponent of 2 in the simplified expression from Step 2. Therefore, option D is not equivalent to the given expression.

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Which expressions are equivalent to $\newline$ $4^{-2}\cdot7^{-2}$ ? $\newline$ Choose $2$ answers: $\newline$ (A) $(4\cdot7)^{-4}$ $\newline$ (B) $\frac{1}{28^{2}}$ $\newline$ (C) $\frac{7^{-2}}{4^{2}}$ $\newline$ (D) $(4\cdot7)^{4}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Which expressions are equivalent to

\newline

4^{-2}\cdot7^{-2}

\newline

Choose

2

answers:

\newline

(A)

(4\cdot7)^{-4}

\newline

(B)

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

\newline

(C)

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

\newline

(D)

(4\cdot7)^{4}

Understand Given Expression: Understand the given expression. $\newline$ We are given the expression $4^{-2}\times7^{-2}$ and we need to find which of the provided options are equivalent to this expression.
Simplify Using Exponents: Simplify the given expression using the property of exponents. $\newline$ When we multiply two exponents with the same negative exponent, we can combine the bases and keep the exponent. $\newline$ $4^{-2} \times 7^{-2} = (4 \times 7)^{-2}$
Check Option A: Check option A: $(4\times7)^{-4}$ $\newline$ This option has a different exponent than what we derived in Step $2$ . Therefore, option A is not equivalent to the given expression.
Check Option B: Check option B: $(1)/(28^{2})$ $\newline$ Rewrite the simplified expression from Step $2$ as a fraction. $\newline$ $(4*7)^{-2} = 1/(4*7)^{2} = 1/(28^{2})$ $\newline$ Option B is equivalent to the given expression.
Check Option C: Check option C: $(7^{-2})/(4^{2})$ $\newline$ This option does not match the simplified expression from Step $2$ because the exponents are not the same for both the numerator and the denominator. Therefore, option C is not equivalent to the given expression.
Check Option D: Check option D: $(4*7)^{4}$ $\newline$ This option has a positive exponent and is raised to the power of $4$ , which is different from the negative exponent of $2$ in the simplified expression from Step $2$ . Therefore, option D is not equivalent to the given expression.