Question

Simplify the expression and eliminate any negative exponents, assuming that all letters denote positive numbers.

(2x^4 * y^(-4/5))^3(8y^2)^(2/3)

I try to post it in equation form too.

Answer 1

Could you draw it out?

Answer 2

\[(2x^4y^\frac{ -4 }{ 5 })^3(8y^2)^\frac{ 2 }{ 3 }\]

Answer 3

if it was \[(a ^{4})^{3}\]
What have you learned to do with the exponents?

Answer 4

Multiply 4 and 3, right?

Answer 5

Yes, what if it was \[(4a ^{4})^{3}\] ?

Answer 6

4 to the third times a to the 12

Answer 7

Yes, what happens with \[(8y ^{2})^{2/3}\] ?

Answer 8

\[8^\frac{ 2 }{ 3 }y ^\frac{ 4 }{ 3 }\]

Answer 9

Ok, so which part do you have trouble with?

Answer 10

Well, the answer in the back of the book is 14, and no matter what I do, i can't get 14! I'll take a picture of my work real quick and maybe you can see what I did then?

Answer 11

Sure

Answer 12

\[ \large (2x^4y^{-4/5})^3(8y^2)^{2/3}=2^3x^{4\times3}y^{-4/5\times3}
8^{2/3}y^{2\times2/3} \]

Answer 13

\[ \large 8x^{12}y^{-12/5}8^{2/3}y^{4/3} \]

Answer 14

\[ \large =8^{1+2/3}x^{12}y^{4/3-12/5}=8^{5/3}x^{12}y^{-16/15} \]