# How do you simplify (7/4)^3?

##### 1 Answer
Apr 26, 2015

${\left(\frac{7}{4}\right)}^{3} = \frac{7}{4} \cdot \frac{7}{4} \cdot \frac{7}{4} = \frac{7 \cdot 7 \cdot 7}{4 \cdot 4 \cdot 4} = {7}^{3} / {4}^{3}$

For any fraction and ${\left(\frac{p}{q}\right)}^{n} = {p}^{n} / {q}^{n}$, so

${\left(\frac{7}{4}\right)}^{3} = {7}^{3} / {4}^{3} = \frac{49 \cdot 7}{16 \cdot 4} = \frac{343}{64}$