# To calculate: \frac{(9a^{3}b^{4})^{\frac{1}{2}}}{15a^{2}b}

To calculate: $\frac{\left(9{a}^{3}{b}^{4}{\right)}^{\frac{1}{2}}}{15{a}^{2}b}$

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Maciej Morrow
Step 1
This algebraic expression needs to be simplified.
$\frac{{\left(9{a}^{3}{b}^{4}\right)}^{\frac{1}{2}}}{15{a}^{2}b}$
Step 2
Our first step would be to distribute the exponent 1/2 on all the terms in the numerator as shown below:
$\frac{{\left(9{a}^{3}{b}^{4}\right)}^{\frac{1}{2}}}{15{a}^{2}b}⇒\frac{{\left(9\right)}^{\frac{1}{2}}{\left({a}^{3}\right)}^{\frac{1}{2}}{\left({b}^{4}\right)}^{\frac{1}{2}}}{15{a}^{2}b}$
Step 3
Our next step is to simplify the exponents in the numerator as shown below:
$\frac{{\left(9\right)}^{\frac{1}{2}}{\left({a}^{3}\right)}^{\frac{1}{2}}{\left({b}^{4}\right)}^{\frac{1}{2}}}{15{a}^{2}b}⇒\frac{3{a}^{\frac{3}{2}}{b}^{2}}{15{a}^{2}b}$
Step 4
Our next step is to split the corresponding terms and write them as numerator/denominator and finally use quotient rule of exponents to simplify them as shown below:
$\frac{3{a}^{\frac{3}{2}}{b}^{2}}{15{a}^{2}b}⇒\frac{3}{15}\cdot \frac{{a}^{\frac{3}{2}}}{{a}^{2}}\cdot \frac{{b}^{2}}{b}$

Step 5
We dont
Jeffrey Jordon