Question

Work out 15^3/2 in surd form

Answer 1

`15 √(15)`

Explanation:

Given:

`15^{(3)/(2)}`

Rewrite the exponent ³/₂ as 1 + ¹/₂ :

`\implies 15^{1+(1)/(2)}`

`\textsf{Apply exponent rule} \quad a^(b+c)=a^b \cdot a^c:`

`\implies 15^(1) \cdot 15^{(1)/(2)}`

`\implies 15 \cdot 15^{(1)/(2)}`

`\textsf{Apply exponent rule} \quad a^{(1)/(2)}=√(a):`

`\implies 15 \cdot √(15)`

`\implies 15 √(15)`