How do you simplify 5^(3/4)5^(1/4)?

1 Answer
Jan 11, 2018

$5$

Explanation:

In algebra we have a process of multiplying with bases and indices.

${x}^{3} \times {x}^{5} = {x}^{3 + 5} = {x}^{8}$

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

Exactly the same applies in this case. The bases are both $5$

${5}^{\frac{3}{4}} \times {5}^{\frac{1}{4}} \text{ } \leftarrow$ bases are the same and multiplying:

Keep the same base and add the indices:

${5}^{\frac{3}{4} + \frac{1}{4}}$

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

$= {5}^{1}$

$= 5$