Higher only · fractional indices

Fractional and
negative indices.
Root, power, flip.

the bottom of the
fraction is the root

reading a fractional index —

a^m/n

bottom number: the root

top number: the power

step 1 of 4

Unit fractions are roots

1. Power ½ means square root.

2. Power ⅓ means cube root.

✓ The denominator tells you the root

25^1/2 = √25 = 5

8^1/3 = ³√8 = 2

16^1/4 = ⁴√16 = 2

step 2 of 4

Root first, then power

1. Cube root of 8 is 2.

2. Then square it: 4.

✓ Root first keeps the numbers small

8^2/3

= (³√8)² root, then power

= 2² = 4

step 3 of 4

Negative: one over

1. The minus sign means reciprocal.

2. It does not make the answer negative.

✓ On a fraction, it flips the fraction

5⁻²

= 15² flip it

= 125

step 4 of 4

All three at once

1. Negative: write it as one over.

2. Fourth root of 16 is 2. Then cube it.

✓ Flip, root, power

16^−3/4

= 116^3/4 flip

= 1(⁴√16)³ root

= 12³ = 18

fractional and negative —

Denominator

which root to take

Numerator

the power, after the root

Negative

one over: the reciprocal

Flip, root, power.
In that order.

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