Question

Which expression is equivalent to (81x4y16)12 for all positive values of x and y?
40.5x4y16

Answer 1

Answer:

$(81x^4y^{16})^{\frac{1}{2}} = 9 x^2 y^8$

Step-by-step explanation:

Given

$(81x^4y^{16})^{\frac{1}{2}}$

Required

Determine an equivalent expression

Express 81 as $9^2$

$(9^2x^4y^{16})^{\frac{1}{2}}$

Apply law of indices

$9^2^{\frac{1}{2}} * x^4^{\frac{1}{2}} * y^{16}^{\frac{1}{2}}$

$9^{\frac{2*1}{2}} * x^{\frac{4*1}{2}} * y^{\frac{16*1}{2}}$

$9^{\frac{2}{2}} * x^{\frac{4}{2}} * y^{\frac{16}{2}}$

$9^1 * x^2 * y^8$

$9 * x^2 * y^8$

$9 x^2 y^8$

Hence:

$(81x^4y^{16})^{\frac{1}{2}} = 9 x^2 y^8$