## Radicals and Rational exponents: 5*cbrt[16] + cbrt[54]

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### Radicals and Rational exponents: 5*cbrt[16] + cbrt[54]

This is from my Algebra/preCalc class and I do not understand how to breakdown and solve this problem. I have thus far been able to solve most problems in this section by using the book examples to work it out and understand them. This problem does not have an example, and I can't figure out how to break it down to the book given answer of: $13\sqrt[3]{2}$

If I could see this worked out step-by-step I feel I would be able to understand the rest like this.

Book Instructions: Add or subtract terms.

$5\sqrt[3]{16}+\sqrt[3]{54}$

I have another problem I am stuck on as well, but will wait until seeing this one to see if I can figure it out from there. Much appreciated.
EricA

Posts: 2
Joined: Mon Sep 06, 2010 3:40 pm

### Re: Radicals and Rational exponents

EricA wrote:Book Instructions: Add or subtract terms.

$5\sqrt[3]{16}+\sqrt[3]{54}$

Hint:

$\sqrt[3]{16}\, =\, \sqrt[3]{8\times 2}\, =\, \sqrt[3]{2^3\, \times\, 2}\, =\, \sqrt[3]{2^3}\,\times\, \sqrt[3]{2}$

$\sqrt[3]{54}\, =\, \sqrt[3]{27\times 3}\, =\, \sqrt[3]{3^3\, \times\, 2}\, =\,\sqrt[3]{3^3}\,\times\, \sqrt[3]{2}$
Stranger_1973

Posts: 21
Joined: Sun Feb 22, 2009 9:56 pm

### Re: Radicals and Rational exponents: 5*cbrt[16] + cbrt[54]

Got it! Thanks for the hint!
EricA

Posts: 2
Joined: Mon Sep 06, 2010 3:40 pm