# How do you determine which is greater 5^3*5^4 (<=>) 5^10?

Sep 30, 2015

${5}^{10}$

Use the laws of indices

#### Explanation:

If two numbers with the same bases but different powers are multiplying, they can be written as the base to the power of the addition of the powers.

In the case of ${5}^{3} \cdot {5}^{4}$,
$5$ is the common base, and
the addition of the powers is $3 + 4$, which equals $7$.

So, ${5}^{3} \cdot {5}^{4} = {5}^{3 + 4}$, which equals ${5}^{7}$

${5}^{10}$ has a greater power than ${5}^{7}$, so
${5}^{10}$ is greater than ${5}^{7}$