# Perform indicated operation and simplify

• Apr 12th 2009, 08:16 AM
Hapa
Perform indicated operation and simplify
(3^4th root of 32a^5) - (a^4th root of 162a)

How do I go about solving this?

Oh, BTW, Happy Easter!
• Apr 12th 2009, 08:50 AM
Soroban
Hello, Hapa!

It's impossible to read what you've typed.
But I'll take a guess at what you meant . . .

Quote:

Simplify: . $3\sqrt[4]{32a^5} - a\sqrt[4]{162a}$
I'll simplify those radicals separately . . .

. . $\sqrt[4]{32a^5} \:=\:\sqrt[4]{16a^4\cdot2a} \:=\:\sqrt[4]{16a^4}\cdot\sqrt[4]{2a} \;=\;2a\sqrt[4]{2a}$

. . $\sqrt[4]{162a} \:=\:\sqrt[4]{81\cdot2a} \:=\:\sqrt[4]{81}\sqrt[4]{2a} \:=\:3\sqrt[4]{2a}$

The problem becomes: . $3\left(2a\sqrt[4]{2a}\right) - a\left(3\sqrt[4]{2a}\right)$

. . . . . . . . . . . . . . . $= \;6a\sqrt[4]{2a} - 3a\sqrt[4]{2a}$

. . . . . . . . . . . . . . . $= \;3a\sqrt[4]{2a}$