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GB-13-05-001 · Fractional indices

Find the exact value of 163416^{\frac{3}{4}}.

Index Laws: Numerical Fractional Indices Booklet p. 17
Method
Use x^(a/b) = (ᵇ√x)ᵃ (power / root):
1) Find the b-th root first
2) Raise the result to the power a
Worked Example (GB-13-05-001)
Booklet p. 17: xpowerroot=(xroot)powerx^{\frac{\text{power}}{\text{root}}} = (\sqrt[\text{root}]{x})^{\text{power}}
163  ←Power (P)4  ←Root (R)=(164)3=(2)3=816^{\frac{3\;\leftarrow\text{Power (P)}}{4\;\leftarrow\text{Root (R)}}} = \left(\sqrt[4]{16}\right)^{3} = (2)^{3} = \mathbf{8}
8