Simplify the following expressions.

[nikeamc44]

125a^15 b^8 c^4 all under a cubed radical?[/code][/tex][/list]

 

[stapel]

...all under a cubed radical?

I'm sorry, but we'll need more information. You say that the expression is inside a radical, and that the radical is them cubed. But what is the index of the radical?

When you reply, please show the steps you have tried so far (even if you think they are wrong).

Thank you.

Eliz.

 

[soroban]

Hello, nikeamc44!

I assume you meant: $\displaystyle \;$ 125a^15 b^8 c^4 all under a cube root.

Use the same routine for simplifying square roots,
$\displaystyle \;\;$except we want factors which are perfect <u>cubes</u>.


\(\displaystyle \L\;\;\sqrt[3]{125\cdot a^{15}\cdot b^8\cdot c^4}\)

\(\displaystyle \L\;\;=\;\sqrt[3]{125(a^{15})(b^6\cdot b^2)(c^3\cdot c)}\)

\(\displaystyle \L\:\;\;=\;\sqrt[3]{(125a^{15} b^6 c^3)(b^2c)}\)

\(\displaystyle \L\;\;\;=\;\sqrt[3]{125a^{15}b^6c^3}\,\cdot\,\sqrt[3]{b^2c}\)

\(\displaystyle \L\;\;\;=\;5a^3b^2c\,\sqrt[3]{b^2c}\)

 

[Gene]

One typo
\(\displaystyle \L\;\;\;=\;5a^3b^2c\,\sqrt[3]{b^2c}\)
should be
\(\displaystyle \L\;\;\;=\;5a^5b^2c\,\sqrt[3]{b^2c}\)
---------------
Gene