Question

Simplify:

`(a^((-1)/4) * a^(7/8))/(root(6)(a^3))`

Answer 1

Given,

`(a^((-1)/4) * a^(7/8))/(root(6)(a^3))`

We have to simplify the given expression.

Thus, `(a^((-1)/4) * a^(7/8))/(root(6)(a^3))`  ...[∴ xⁿ × x^m = x^{n + m}]

⇒ `a^((-1)/4 + 7/8)/((a^3)^(1/6)`  ...`[∴ root(n)(x) = x^(1/n)]`

⇒ `a^(((-1)/4 xx 2/2) + 7/8)/((a)^(3 xx 1/6)`

⇒ `(a^((-2)/8 + 7/8))/(a)^(1/2)`

⇒ `a^(5/8)/a^(1/2)`  ...`[∴ x^n/x^m = x^(n - m)]`

⇒ `a^(5/8 - 1/2)`

⇒ `a^(5/8 - (1/2 xx 4/4)) = a^(5/8 - 4/8) = a^(1/8)`

Hence, `(a^((-1)/4) * a^(7/8))/(root(6)(a^3)) = a^(1/8)`.