# How do you simplify and write  5^2 times 5^4 with positive exponents?

May 18, 2018

${5}^{6}$

#### Explanation:

The first law of indices you usually learn is the one about multiplying.

'If the bases are the same and you are multiplying, add the indices.'

${x}^{m} \times {x}^{n} = {x}^{m + n}$

In this case the bases are both $5$

${5}^{2} \times {5}^{4} = {5}^{2 + 4} = {5}^{6}$

To see why this is so, write them out in expanded form:

${5}^{2} \times {5}^{4} = \left(5 \times 5\right) \times \left(5 \times 5 \times 5 \times 5\right) = {5}^{6}$