# How do you simplify (3/4)^-1 and write it using only positive exponents?

Mar 29, 2017

${\left(\frac{3}{4}\right)}^{-} 1 = {\left(\frac{4}{3}\right)}^{1}$ to write it using only positive exponents

#### Explanation:

The negative exponent in this expression requires that we invert the fraction, which is the same as taking the inverse of the value of the fraction.

The inverse of $\frac{3}{4} = \frac{1}{\frac{3}{4}} = \frac{1}{1} \cdot \frac{4}{3} = \frac{4}{3}$

Then;${\left(\frac{3}{4}\right)}^{-} 1 = {\left(\frac{4}{3}\right)}^{1}$ to write it using only positive exponents

The final simplification would be: ${\left(\frac{3}{4}\right)}^{-} 1 = {\left(\frac{4}{3}\right)}^{1} = \left(\frac{4}{3}\right) = 1 \frac{1}{3}$