When you simplify an algebraic expression like a53⋅a14 , you know that the bases of the expressions must be the same. You also n

Question

1 month ago

7

eed to rewrite the exponents so that they have a common denominator. Explain why you need to find the common denominator to simplify.

1 answer:

babunello [11.8K] · Answer 1 · 2026-04-03T21:33:04+03:00

6 0

Response:

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

Detailed explanation:

Given

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

Necessary

Assess

This will be tackled using exponent laws:

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

Thus, we observe:

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

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

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

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

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