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$Express the following fraction in simplest form using only positive exponents. (2h^(5))/((3h^(2))^(2)) Answer:$

Express the following fraction in simplest form using only positive exponents. $\newline$ $\frac{2 h^{5}}{\left(3 h^{2}\right)^{2}}$ $\newline$ Answer:

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Multiplication with rational exponents

Full solution

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

\newline

\frac{2 h^{5}}{\left(3 h^{2}\right)^{2}}

\newline

Answer:

Simplify Denominator: Simplify the denominator. $\newline$ The denominator is $(3h^{2})^{2}$ . When raising a power to a power, you multiply the exponents. $\newline$ $(3h^{2})^{2} = 3^{2} \times (h^{2})^{2}$ $\newline$ $= 9 \times h^{2\times2}$ $\newline$ $= 9 \times h^{4}$
Write Fraction: Write the fraction with the simplified denominator. $\newline$ Now we have the fraction as: $\newline$ $(\frac{2h^{5}}{9h^{4}})$
Cancel Common Factors: Simplify the fraction by canceling out common factors. $\newline$ We can divide both the numerator and the denominator by $h^{4}$ since $h^{4}$ is a common factor. $\newline$ $(2h^{5}) / (9h^{4}) = (2h^{5-4}) / (9)$ $\newline$ $= (2h^{1}) / (9)$ $\newline$ $= 2h / 9$

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