# Which expression is equivalent to 5^-8*5^3?

Dec 9, 2016

${5}^{-} 5$ or $\frac{1}{5} ^ 5$ or $\frac{1}{3125}$

#### Explanation:

Using the rules for exponents ($\textcolor{red}{{x}^{a} \cdot {x}^{b} = {x}^{a + b}}$):

${5}^{-} 8 \cdot {5}^{3} \to {5}^{- 8 + 3} \to {5}^{-} 5$

We can convert further using another rule for exponents ($\textcolor{red}{{x}^{-} a = \frac{1}{x} ^ - a}$):

${5}^{-} 5 \to \frac{1}{5} ^ 5$

And then converting the exponent to a number gives:

$\frac{1}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5} \to \frac{1}{3125}$