Calculating with Fractional Indices

Processing math: 100%

Number
Algebra
Ratio
Geometry
Probability
Statistics

For a fractional index, the numerator is a power term, and the denominator is a root term.

$27^frac(2)(3)$ means square 27 then cube root the answer (You can also cube root 27 then square the answer; the order does not matter). Choose the easiest calculation. In this instance, the cube root of 27 is 3, and 3 squared is 9.

Example 1

Simplify $sqrt(2) xx root(4)2$ , and show with a fractional index.

$sqrt(2) xx root(4)2$

= $2^frac(1)(2) xx 2^frac(1)(4)$

add indices (Laws of Indices)

= $2^frac(3)(4)$

Answer: $2^frac(3)(4)$

Example 2

Simplify √5 ÷ 25. Leave the index as a fraction.

$sqrt(5) ÷ 25$

$5^frac(1)(2) ÷ 5^2$

$5^((frac(1)(2) - 2))$

$5^-frac(3)(2)$

Answer: $5^(frac(-3)(2)$

Return to Number menu