ccss.hsa1e-qv.12 - Evaluate negative integers raised to rational exponents

Sangeetha Pulapaka (last edited 3 years ago) (Expert, Educator @Qalaxia)

STEP 1: Recall what are exponents

STEP 2: Recall the rules of exponents

STEP 3: Evaluate

-16^\frac{3}{4} = (-16)^\frac{3}{4} = (-16^\frac{1}{4})^{3}

Using the fractional exponent rule

(-16^\frac{1}{4})^{3} = [math]-\sqrt[4]{(16)^{3}}[/math] = [math]-\sqrt[4]{(2^{4})^{3}}[/math] = -2^{3}= -8

Skills you may want to recall:

How to find the fourth root of a number

How to multiply two three times