which expression is equivalent to $\frac{9x^{5}y^{16}}{45x^{5}y^{4}}$?\n$\frac{y^{12}}{5}$\n$\frac{y^{12}}{36…

which expression is equivalent to $\frac{9x^{5}y^{16}}{45x^{5}y^{4}}$?\n$\frac{y^{12}}{5}$\n$\frac{y^{12}}{36}$\n$\frac{xy^{4}}{5}$\n$\frac{xy^{4}}{36}$

which expression is equivalent to $\frac{9x^{5}y^{16}}{45x^{5}y^{4}}$?\n$\frac{y^{12}}{5}$\n$\frac{y^{12}}{36}$\n$\frac{xy^{4}}{5}$\n$\frac{xy^{4}}{36}$

Answer

Explanation:

Step1: Simplify the coefficient

Divide 9 by 45: $\frac{9}{45}=\frac{1}{5}$

Step2: Use exponent - rule for $x$ terms

For $\frac{x^{5}}{x^{5}}$, according to the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$, we have $x^{5-5}=x^{0}=1$

Step3: Use exponent - rule for $y$ terms

For $\frac{y^{16}}{y^{4}}$, using the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$, we get $y^{16 - 4}=y^{12}$

Step4: Combine the results

The simplified expression is $\frac{1\times1\times y^{12}}{5}=\frac{y^{12}}{5}$

Answer:

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