Which expression is equivalent to (4^(-2)*4^(6))^(-5)? 4^(-20) 4^(-17) 4^(-16) 4^(60)

Simplify Exponents: Simplify the expression inside the parentheses by adding the exponents of like bases. According to the exponent rules, when multiplying powers with the same base, you add the exponents. So, 4^(-2) * 4^(6) becomes 4^(-2 + 6). Calculation: -2 + 6 = 4 Therefore, the expression simplifies to 4^(4).Apply Outer Exponent: Apply the outer exponent to the simplified base and exponent. Now we have (4^(4))^(-5). According to the exponent rules, when raising a power to a power, you multiply the exponents. So, 4^(4 * -5) is the next step. Calculation: 4 * -5 = -20 Therefore, the expression simplifies to 4^(-20).

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Which expression is equivalent to
(4^(-2)*4^(6))^(-5)?

4^(-20)

4^(-17)

4^(-16)

4^(60)

Which expression is equivalent to $\left(4^{-2} \cdot 4^{6}\right)^{-5} ?$ $\newline$ $4^{-20}$ $\newline$ $4^{-17}$ $\newline$ $4^{-16}$ $\newline$ $4^{60}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Which expression is equivalent to

\left(4^{-2} \cdot 4^{6}\right)^{-5} ?

\newline

4^{-20}

\newline

4^{-17}

\newline

4^{-16}

\newline

4^{60}

Simplify Exponents: Simplify the expression inside the parentheses by adding the exponents of like bases. $\newline$ According to the exponent rules, when multiplying powers with the same base, you add the exponents. $\newline$ So, $4^{-2} \times 4^{6}$ becomes $4^{-2 + 6}$ . $\newline$ Calculation: $-2 + 6 = 4$ $\newline$ Therefore, the expression simplifies to $4^{4}$ .
Apply Outer Exponent: Apply the outer exponent to the simplified base and exponent. $\newline$ Now we have $(4^{4})^{(-5)}$ . According to the exponent rules, when raising a power to a power, you multiply the exponents. $\newline$ So, $4^{(4 \times -5)}$ is the next step. $\newline$ Calculation: $4 \times -5 = -20$ $\newline$ Therefore, the expression simplifies to $4^{(-20)}$ .