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

What is the simplest form of:

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


I cannot seem to find the answer. The actual answer is [tex]27x\sqrt[8]{x^{4}y^3 }[/tex] 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

Respuesta :

Answer:

See below.

Step-by-step 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)