Simplify((16)/(81)x^(16)\right))^{(1)/(2)}

Question

Simplify
`((16)/(81)x^(16)\right))^{(1)/(2)}`

Answer 1

The answer is = 4x^8/9

Answer 2

`\sf (4)/(9)x^8`

Explanation:

Law of exponents:

`\sf (a*b)^m = a^m *b^m\\\\(a^m)^n =a^(m*n)`

16 = 4 *4 = 4²

81 = 9 *9 = 9²

`\sf\left ((16)/(81)x^(16)\right)^{(1)/(2)}= \left((4^2)/(9^2)x^(16)\right)^{(1)/(2)}`

`\sf =\frac{4^{2*(1)/(2)}}{9^{2*(1)/(2)}}*x^{16*(1)/(2)}\\\\=(4)/(9)x^8`