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$Express the following fraction in simplest form using only positive exponents. (20z^(4))/(4(z^(2))^(3)) Answer:$

Express the following fraction in simplest form using only positive exponents. $\newline$ $\frac{20 z^{4}}{4\left(z^{2}\right)^{3}}$ $\newline$ 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^{4}}{4\left(z^{2}\right)^{3}}

\newline

Answer:

Simplify Base and Exponent: Simplify the base and exponent in the denominator. $\newline$ The denominator has a power raised to a power, which means we multiply the exponents. $(z^{2})^{3} = z^{2*3} = z^{6}$ .
Divide Coefficients and Exponents: Divide the coefficients and simplify the exponents. $\newline$ We have $20z^{4}$ in the numerator and $4z^{6}$ in the denominator. Dividing the coefficients gives us $\frac{20}{4} = 5$ . For the variables, we subtract the exponents in the denominator from the exponents in the numerator: $z^{4-6} = z^{-2}$ .
Write with Positive Exponents: Write the expression with only positive exponents. $\newline$ Since we cannot have negative exponents in the final answer, we rewrite $z^{-2}$ as $1/z^{2}$ . The final expression is $5 \times 1/z^{2}$ or $5/z^{2}$ .

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