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$Express the following fraction in simplest form using only positive exponents. (20z^(3))/((4z^(5))^(4)) Answer:$

Express the following fraction in simplest form using only positive exponents. $\newline$ $\frac{20 z^{3}}{\left(4 z^{5}\right)^{4}}$ $\newline$ Answer:

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Simplify variable expressions using properties

Full solution

Q. Express the following fraction in simplest form using only positive exponents.

\newline

\frac{20 z^{3}}{\left(4 z^{5}\right)^{4}}

\newline

Answer:

Simplify base of denominator: Simplify the base of the denominator. $\newline$ We have $(4z^{5})^{4}$ , which means we need to apply the power of a power rule: $(a^{b})^{c} = a^{b*c}$ . $\newline$ So, $(4z^{5})^{4}$ becomes $4^{4} \times z^{5*4} = 256z^{20}$ .
Divide numerator by denominator: Simplify the fraction by dividing the numerator by the denominator. $\newline$ We have $(20z^{3}) / (256z^{20})$ . $\newline$ First, divide the coefficients: $20 / 256 = 5 / 64$ after simplifying. $\newline$ Then, subtract the exponents of $z$ : $z^{3 - 20} = z^{-17}$ , since when dividing like bases you subtract the exponents.
Write final expression: Write the final expression using only positive exponents. $\newline$ Since we cannot have negative exponents in the final answer, we rewrite $z^{-17}$ as $1/z^{17}$ . $\newline$ So, the final expression is $(5 / 64) * (1/z^{17})$ or $5 / (64z^{17})$ .

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