Rational exponents, step by step
A fractional exponent is a root and a power in one symbol: the bottom says which root, the top says what to raise it to.
The question
What is 8 to the power 4/3?
8^(4/3)
∛8 = 2
2⁴ = 16
8^(4/3) = 16
- The BOTTOM of the exponent says which root to take, so the cube root of 8 comes first. Root before power, always — the other order works and makes the numbers enormous.
- The TOP says what to raise it to. 2 to the power 4 is 16.
- So 8^(4/3) is 16.
How it works.
- 01
The BOTTOM of the exponent says which root to take, so the cube root of 8 comes first. Root before power, always — the other order works and makes the numbers enormous.
- 02
The TOP says what to raise it to. 2 to the power 4 is 16.
- 03
So 8^(4/3) is 16.