Question

(√2)^3

`(\sqrt{2) {?}^(3 \\)`
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Answer 1

`\sf \left(√(2)\right)^3\\\\\\\\\boxed{\sf \mathrm{Apply\:radical\:rule}:\quad √(a)=a^{(1)/(2)}}\\\\\\\\\sf \left(2^{(1)/(2)}\right)^3\\\\\\\\\boxed{\sf\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^(bc) }\\\\\\\\\sf \sf 2^{(1)/(2)\cdot \:3}\\\\\\\\\sf 2^{(3)/(2)}\\\\\\\\\sf 2^{(3)/(2)}=2^{1+(1)/(2)}\\\\\\\\\sf 2^{1+(1)/(2)}\\\\\\\\\boxed{\sf \mathrm{Apply\:exponent\:rule}:\quad \:x^(a+b)=x^ax^b}\\\\\\\\\sf`

`\sf 2 ^1\cdot \:2^{(1)/(2)}\\\\\\\\\boxed{\sf \mathrm{Refine}}\\\\\\\\\boxed{\sf =2√(2)}`