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 and the properties of exponents. The given expression is 4^(-2)*7^(-2). According to the properties of exponents, when we multiply two powers with the same exponent, we can add the bases and keep the exponent the same.Apply Exponent Property: Apply the property of exponents to the given expression. 4^(-2)*7^(-2) can be written as (4*7)^(-2) because we are multiplying two numbers with the same negative exponent.Check Answer Choices: Check the answer choices to see which ones are equivalent to (4*7)^(-2). A) (4*7)^(-4) is not equivalent because the exponent is -4 instead of -2. B) (1)/(28^(2)) is equivalent because (4*7) is 28, and raising it to the power of -2 is the same as taking the reciprocal of 28 squared. C) (7^(-2))/(4^(2)) is not equivalent because the bases are being divided, not multiplied, and the exponents are not the same. D) (4*7)^(4) is not equivalent because the exponent is positive 4, not negative 2.Confirm Correct Answers: Confirm the correct answers by simplifying the expressions. (4*7)^(-2) simplifies to (28)^(-2), which is the same as 1/(28^2), so option B is correct. None of the other options simplify to the same expression as the given one.

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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)

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

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Which expressions are equivalent to

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

\newline

Choose

2

answers:

\newline

(4 \cdot 7)^{-4}

\newline

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

\newline

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

\newline

(4 \cdot 7)^{4}

Understand Given Expression: Understand the given expression and the properties of exponents. $\newline$ The given expression is $4^{-2}\times7^{-2}$ . According to the properties of exponents, when we multiply two powers with the same exponent, we can add the bases and keep the exponent the same.
Apply Exponent Property: Apply the property of exponents to the given expression. $4^{-2}\times7^{-2}$ can be written as $(4\times7)^{-2}$ because we are multiplying two numbers with the same negative exponent.
Check Answer Choices: Check the answer choices to see which ones are equivalent to $(4\times7)^{-2}$ . $\newline$ A) $(4\times7)^{-4}$ is not equivalent because the exponent is $-4$ instead of $-2$ . $\newline$ B) $\frac{1}{28^{2}}$ is equivalent because $(4\times7)$ is $28$ , and raising it to the power of $-2$ is the same as taking the reciprocal of $28$ squared. $\newline$ C) $\frac{7^{-2}}{4^{2}}$ is not equivalent because the bases are being divided, not multiplied, and the exponents are not the same. $\newline$ D) $(4\times7)^{-4}$ $0$ is not equivalent because the exponent is positive $(4\times7)^{-4}$ $1$ , not negative $-2$ .
Confirm Correct Answers: Confirm the correct answers by simplifying the expressions. $\newline$ $(4\times7)^{-2}$ simplifies to $(28)^{-2}$ , which is the same as $1/(28^2)$ , so option $B$ is correct. $\newline$ None of the other options simplify to the same expression as the given one.