Select the equivalent expression. (2^(-4)*z^(-3))^(5)=? Choose 1 answer: (A) 2z^(2) (B) 2^(20)*z^(15) (C) (1)/(2^(20)*z^(15))

Apply power of power rule: Apply the power of a power rule. The power of a power rule states that (a^m)^n = a^(m*n). We will apply this rule to both 2^(-4) and z^(-3). (2^(-4)*z^(-3))^5 = 2^(-4*5) * z^(-3*5)Perform exponent multiplication: Perform the multiplication for the exponents. Now we multiply the exponents inside the parentheses by 5. 2^(-4*5) * z^(-3*5) = 2^(-20) * z^(-15)Rewrite using negative exponent rule: Rewrite the expression using the negative exponent rule. The negative exponent rule states that a^(-n) = 1/(a^n). We will apply this rule to both 2^(-20) and z^(-15). 2^(-20) * z^(-15) = 1/(2^20) * 1/(z^15)Combine fractions: Combine the fractions. Since both fractions have a numerator of 1, we can combine them into a single fraction. 1/(2^20) * 1/(z^15) = 1/(2^20 * z^15)

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Select the equivalent expression. $\newline$ $(2^{-4} \cdot z^{-3})^{5}= ?$ $\newline$ Choose $1$ answer: $\newline$ (A) $2z^{2}$ $\newline$ (B) $2^{20} \cdot z^{15}$ $\newline$ (C) $\frac{1}{2^{20} \cdot z^{15}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

(2^{-4} \cdot z^{-3})^{5}= ?

\newline

Choose

1

answer:

\newline

(A)

2z^{2}

\newline

(B)

2^{20} \cdot z^{15}

\newline

(C)

\frac{1}{2^{20} \cdot z^{15}}

Apply power of power rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(a^m)^n = a^{m*n}$ . We will apply this rule to both $2^{-4}$ and $z^{-3}$ . $\newline$ $(2^{-4}*z^{-3})^5 = 2^{-4*5} * z^{-3*5}$
Perform exponent multiplication: Perform the multiplication for the exponents. $\newline$ Now we multiply the exponents inside the parentheses by $5$ . $\newline$ $2^{(-4\times5)} \times z^{(-3\times5)} = 2^{(-20)} \times z^{(-15)}$
Rewrite using negative exponent rule: Rewrite the expression using the negative exponent rule. $\newline$ The negative exponent rule states that $a^{-n} = \frac{1}{a^n}$ . We will apply this rule to both $2^{-20}$ and $z^{-15}$ . $\newline$ $2^{-20} \cdot z^{-15} = \frac{1}{2^{20}} \cdot \frac{1}{z^{15}}$
Combine fractions: Combine the fractions. $\newline$ Since both fractions have a numerator of $1$ , we can combine them into a single fraction. $\newline$ $\frac{1}{2^{20}} \times \frac{1}{z^{15}} = \frac{1}{2^{20} \times z^{15}}$