Mathematics: Which expression is equivalent to 9x^5y^16/45x^5y^4

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Which expression is equivalent to 9x^5y^16/45x^5y^4

alowery89

04.01.2022

An equivalent expression to the given expression $\frac{9x^5y^{16}}{45x^5y^4}$ is $\frac{y^{12}}{5}$

Step-by-step explanation:

Given : Expression $\frac{9x^5y^{16}}{45x^5y^4}$

We have to find an equivalent expression to the given expression $\frac{9x^5y^{16}}{45x^5y^4}$

Consider the given expression $\frac{9x^5y^{16}}{45x^5y^4}$

Cancel the common factor 9, we have,

$=\frac{x^5y^{16}}{5x^5y^4}$

Cancel the common factor x^5 , we have,

$=\frac{y^{16}}{5y^4}$

$\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}\:=\:x^{a-b}$

We have, $\frac{y^{16}}{y^4}=y^{16-4}=y^{12}$

Thus, we get,

$=\frac{y^{12}}{5}$

Thus, An equivalent expression to the given expression $\frac{9x^5y^{16}}{45x^5y^4}$ is $\frac{y^{12}}{5}$

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