# How do you write 5*5^-5 using only positive exponents?

Oct 11, 2017

$\frac{1}{5} ^ 4$

#### Explanation:

$5 \cdot {5}^{-} 5$

According to indices $a \times a = {a}^{1 + 1} = {a}^{2}$

We are going to apply that here..

${5}^{1} \cdot {5}^{-} 5$

${5}^{1 - 5}$

${5}^{-} 4$

$\frac{1}{5} ^ 4 \to \text{Positive Exponent}$

$\frac{1}{625}$

Only positive exponent?

It can't be positive exponent cause it contains a negative exponent in the given question..

To make it a positive exponent is when the positive exponent value is greater than the negative exponent value..

The only positive exponent there is $\Rightarrow \frac{1}{5} ^ 4$ which has a positive exponent of $4$