Question

Help Me Simplify the expression

Answer 1

What is the problem?

Answer 2

o_O that's hard, sorry, I'm not up to that yet. :(

Answer 3

and rewrite it in rational exponent form

Answer 4

okay

Answer 5

Okay, you basically need to know 3 rules:

\(\Large\color{black}{ \displaystyle x^{\color{red}{\rm a}} \times x^{\color{blue}{\rm b}}=x^{\color{red}{\rm a}+\color{blue}{\rm b}}\\[0.5em] }\)
\(\Large\color{black}{ \displaystyle x^{\color{red}{\rm a}} \div x^{\color{blue}{\rm b}}=x^{\color{red}{\rm a}-\color{blue}{\rm b}}\\[0.5em] }\)
\(\Large\color{black}{ \displaystyle \sqrt[\color{blue}{\rm b}]{x^{\color{red}{\rm a}}}= x^{\color{red}{\rm a}/\color{blue}{\rm b}} }\)

Answer 6

hmmm actaully... .I kinda miss a couple of fellows, the 3 and 4 at the bottom... lemme rewrite it a bit in a sec

Answer 7

hmmm
\(\large {
\cfrac{x^{\frac{2}{3}}\cdot 24y\cdot \sqrt[4]{y^3}}{3x^2\cdot 4\sqrt[3]{x^2}}
\\ \quad \\

a^{\frac{{\color{blue} n}}{{\color{red} m}}} \implies \sqrt[{\color{red} m}]{a^{\color{blue} n}} \qquad \qquad

\sqrt[{\color{red} m}]{a^{\color{blue} n}}\implies a^{\frac{{\color{blue} n}}{{\color{red} m}}}\qquad thus
\\ \quad \\
\cfrac{x^{\frac{2}{3}}\cdot 24y\cdot \sqrt[4]{y^3}}{3x^2\cdot 4\sqrt[3]{x^2}}\implies
\cfrac{x^{\frac{2}{3}}\cdot 24y\cdot y^{\frac{3}{4}}}{3x^2\cdot 4x^{\frac{2}{3}}}\qquad and\ then
\\ \quad \\
a^{-\frac{{\color{blue} n}}{{\color{red} m}}} =
\cfrac{1}{a^{\frac{{\color{blue} n}}{{\color{red} m}}}} \implies \cfrac{1}{\sqrt[{\color{red} m}]{a^{\color{blue} n}}}\qquad\qquad

% radical denominator
\cfrac{1}{\sqrt[{\color{red} m}]{a^{\color{blue} n}}}= \cfrac{1}{a^{\frac{{\color{blue} n}}{{\color{red} m}}}}\implies a^{-\frac{{\color{blue} n}}{{\color{red} m}}} \qquad thus
\\ \quad \\

\cfrac{x^{\frac{2}{3}}\cdot 24y^1\cdot y^{\frac{3}{4}}}{3^1x^2\cdot 4^1x^{\frac{2}{3}}}\implies
x^{\frac{2}{3}}\cdot 24y^1\cdot y^{\frac{3}{4}}\cdot 3^{-1}x^{-2}\cdot 4^{-1}x^{-\frac{2}{3}}
\\ \quad \\
\implies \cfrac{x^{\frac{2}{3}\cdot}\cdot x^{-2}\cdot x^{-\frac{2}{3}}\cdot 24y^1\cdot y^{\frac{3}{4}\cdot } }{3^1\cdot 4^1}
}\)

Answer 8

anyhow, so use the same-base exponent rule
and see what you can cancel out from the fraction

Answer 9

It says rewrite it in rational exponent form @jdoe0001

Answer 10

well, take a look, is all in rational exponents :)

Answer 11

you just need to simplify it