Question

Use the law of exponents to rewrite and simplify the expression.

$\frac{{\left(6y^3\right)}^4}{2y^5}$

Answer 1

To simplify the given expression:

Using the law of exponents to simplify the given expression in below:

$\begin{array}{rcl}\frac{{\left(6y^3\right)}^4}{2y^5}& =& \frac{6^4\times {\left(y^3\right)}^4}{2y^5}\left[\text{Power of a product rule:}{\left(\text{ab}\right)}^{\text{m}}={\left(\text{a}\right)}^{\text{m}}\times {\left(\text{b}\right)}^{\text{m}}\right]\\ & \Rightarrow & \frac{{\left(6y^3\right)}^4}{2y^5}=\frac{6^4\times y^{3\times 4}}{2y^5}\left[\text{Power of a power rule}:{\left({\text{a}}^{\text{m}}\right)}^{\text{n}}={\text{a}}^{\text{m}\times \text{n}}\right]\\ & \Rightarrow & \frac{{\left(6y^3\right)}^4}{2y^5}=\frac{1296\times y^{12}}{2y^5}\left[\text{Simplifying}\right]\\ & \Rightarrow & \frac{{\left(6y^3\right)}^4}{2y^5}=\frac{1296\times y^{12-5}}{2}\left[\text{Quotient rule}:\frac{{\text{a}}^{\text{m}}}{{\text{a}}^{\text{n}}}={\text{a}}^{\text{m-n}}\right]\\ \therefore \frac{{\left(6y^3\right)}^4}{2y^5}& =& 648y^7\left[\text{Simplifying}\right]\end{array}$

Hence, the answer is $\begin{array}{l}\mathbf{648}{\mathit{y}}^{\mathbf{7}}\end{array}$.