Question

When you simplify an algebraic expression like a53⋅a14 , you know that the bases of the expressions must be the same. You also need to rewrite the exponents so that they have a common denominator. Explain why you need to find the common denominator to simplify.

Answer 1

Answer:

$a^{\frac{5}{3}}.a^{\frac{1}{4}} = a^{\frac{23}{12}}$

Step-by-step explanation:

Given

$a^{\frac{5}{3}}.a^{\frac{1}{4}}$

Required

Evaluate

This will be solved using laws of indices:

$a^m * a^n = a^{m+n}$

So, we have:

$a^{\frac{5}{3}}.a^{\frac{1}{4}} = a^{\frac{5}{3}} * a^{\frac{1}{4}}$

$a^{\frac{5}{3}}.a^{\frac{1}{4}} = a^{\frac{5}{3} + \frac{1}{4}}$

$a^{\frac{5}{3}}.a^{\frac{1}{4}} = a^{\frac{20}{12} + \frac{3}{12}}$

$a^{\frac{5}{3}}.a^{\frac{1}{4}} = a^{\frac{20 + 3}{12}}$

$a^{\frac{5}{3}}.a^{\frac{1}{4}} = a^{\frac{23}{12}}$