Question

Given that a^­­b = x, evaluate a^(b+2)

Answer 1

`\huge\boxed{a^(b+2)=a^2x=x^{(b+2)/(b)}}`

Explanation:

`a^b=x\qquad(*)\\\\a^b=x\to\left(a^b\right)^(1)/(b)=x^(1)/(b)\\\\\text{use}\ (a^n)^m=a^(nm)\\\\a^{(b)\left((1)/(b)\right)}=x^(1)/(b)\to a=x^(1)/(b)\qquad(**)\\\\a^(b+2)\qquad\text{use}\ a^n\cdot a^m=a^(n+m)\\\\a^(b+2)=a^b\cdot a^2\\\\\text{From (*) and (**)}:\\\\a^(b+2)=x\cdot\left(x^(1)/(b)\right)^2\\\\\text{use}\ (a^n)^m=a^(nm)\\\\a^(b+2)=x\cdot x^{\left((1)/(b)\right)(2)}\\\\a^(b+2)=x\cdot x^{(2)/(b)}\\\\\text{use}\ a^n\cdot a^m=a^(n+m)`

`a^(b+2)=x^{1+(2)/(b)}\\\\a^(b+2)=x^{(b)/(b)+(2)/(b)}\\\\a^(b+2)=x^{(b+2)/(b)}`

Answer 2

a²x

Explanation:

a^(b+2)

a^b × a^2

x × a²

a²x