# How do you simplify 3^-1*5^-2?

Jan 3, 2017

See full explanation of the simplification process below

#### Explanation:

To simplify this expression we first need to use one of the rules for exponents:

$\textcolor{red}{{x}^{a} = \frac{1}{x} ^ \left(- a\right)}$

Using this rule we can rewrite this problem as:

$\frac{1}{{3}^{- - 1} \cdot {5}^{- - 2}} = \frac{1}{{3}^{1} \cdot {5}^{2}}$

We know ${x}^{1} = x$ so we can rewrite this as"

$\frac{1}{3 \times 5 \times 5} = \frac{1}{75}$