Question

nothing

Answer 1

Where exactly are you stuck?

Answer 2

http://www.wyzant.com/resources/lessons/math/algebra/properties_of_algebra

This gives names to most of the rules you need to use

Answer 3

Just go through each simplification step by step and write what property you used, but yeah to be honest I dont have much experience describing mathematical manipulations.

Answer 4

hmmm

Answer 5

hmm let's try the 1st one.... what would you get for the numerator on this one \(\bf \large \cfrac{x^{\frac{4}{3}}\cdot x^{\frac{7}{3}} }{x^{\frac{2}{3}}}\quad ?\)

Answer 6

we don't necessarily expect you to be great at it, just to do some footwork

Answer 7

the numerator on the 1st one, should be something you should already know

Answer 8

same base, different exponents

Answer 9

I can still try to help you,

for the first manipulation

\[\frac{x^4}{x^2} = x^4x^{-2}\]

"The first step of the simplification involves the elimination of the denominator by writing the exponent as a negative, in order to manipulate the exponents.

x^4x^2 = x^(4+2)

In the second step The exponents are added together, this can be done because their base are the same.

Just drone on like that I suppose?

Answer 10

I just was too lazy to write out your problem so I just wrote out a simpler one that is pretty much the same

Answer 11

yeah

Answer 12

"The first step of the simplification involves the elimination of the denominator by writing the exponent as a negative, in order to manipulate the exponents further."

Answer 13

it isnt really hard just go through each step of the manipulation and explain it in words. Expressing the denominators exponent as a negative to bring it up to the numerator, is a way of taking it out of its fractional form.

Answer 14

\(\bf \Large {\cfrac{x^{\frac{4}{3}}\cdot x^{\frac{7}{3}} }{x^{\frac{2}{3}}}\implies \cfrac{x^{\frac{4}{3}+\frac{7}{3}}}{x^{\frac{2}{3}}}\implies \cfrac{x^{\frac{11}{3}}}{x^{\frac{2}{3}}}\\ \quad \\
\cfrac{x^{\frac{11}{3}}}{1}\cdot \cfrac{1}{x^{\frac{2}{3}}}\implies \cfrac{x^{\frac{11}{3}}}{1}\cdot x^{-\frac{2}{3}}\implies x^{\frac{11}{3}}\cdot x^{-\frac{2}{3}}\\ \quad \\
\implies x^{\frac{11}{3}-\frac{2}{3}}}\)

Answer 15

No problem :) if you get stuck feel free to ask for further assistance

Answer 16

the 2nd one is very straightforward \(\bf \large \sqrt[5]{x^4\cdot x^5\cdot x^6}\implies \sqrt[5]{x^{4+5+6}}\)

Answer 17

3rd one is \(\bf \large \left(\sqrt[7]{x}\right)^{21}\implies \sqrt[7]{x^{21}}\)

Answer 18

4th one \(\bf \large {x^{\frac{1}{3}}\cdot x^{\frac{2}{3}}\cdot x^{\frac{4}{3}}\cdot \sqrt[3]{x}\\ \quad \\
\textit{keep in mind that }a^{\frac{n}{m}} = \sqrt[m]{a^n}\qquad thus\\ \quad \\
\sqrt[3]{x}\implies x^{\frac{1}{3}}}\)