Question

Please help. This pertains to radical exponents (Algebra 2)

What is the simplest form of:


`(9x\sqrt[4]{y})^(3/2)`


I cannot seem to find the answer. The actual answer is
`27x\sqrt[8]{x^(4)y^3 }` but I don't understand how to get that answer. Can you please help me? Maybe write out how you actually get it? I need help

Answer 1

See below.

Explanation:

First convert the radical to a fractional exponent.

Examples of this: √ x = x^1/2.

(∛y)^4 = y ^4/3 - note that the exponent's numerator is the power(4 in this case) and the radical is the denominator).

(9x⁴√y)^3/2

= 9^3/2 * x^3/2 * y(1/4*3/2)

= 3^3 x^3/2 y^3/8

= 27x^3/2y^3/8

= 27 x^12/8 y^3/8

= 27x^8/8 x^4/8 y^3/8

= 27x ⁸√ (x^4 y^3)