# How do you simplify (16/25)^(3/2)?

Feb 7, 2016

$\frac{64}{125}$

#### Explanation:

Remember that ${x}^{\frac{3}{2}} = {\sqrt{x}}^{3}$

With this in mind we can re-write the above expression as:

${\left(\frac{16}{25}\right)}^{\frac{3}{2}} = {\sqrt{\frac{16}{25}}}^{3}$

Don't forget that $16$ and $25$ are square numbers so by taking their square root we can cancel the radical sign over the fraction to get:

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

And now simply cube the numbers inside the brackets:

${\left(\frac{4}{5}\right)}^{3} = \frac{64}{125}$

Feb 7, 2016

$\frac{64}{125}$

#### Explanation:

I shall apply the following 2 laws of exponents :

• ${\left(\frac{a}{b}\right)}^{n} = {a}^{n} / {b}^{n}$
• ${a}^{\frac{m}{n}} = \sqrt[n]{{a}^{m}}$

$\therefore {\left(\frac{16}{25}\right)}^{\frac{3}{2}} = \frac{{16}^{\frac{3}{2}}}{25} ^ \left(\frac{3}{2}\right)$

$= \frac{\sqrt{{16}^{3}}}{\sqrt{{25}^{3}}}$

$= {4}^{3} / {5}^{3}$

$= \frac{64}{125}$