Question

Chapter 5:Indices and Logarithms
@perl

Answer 1

\[(-\frac{ 3 }{ 8 })^{-\frac{ 2 }{ 3 }}\]

Answer 2

Find the value of the following.

Answer 3

because of the negative exponent you can flip the contents of the fraction

Answer 4

(-3/8)^(-2/3) = (-8/3)^(2/3)

Answer 5

okay

Answer 6

\[-\frac{ 8^{\frac{ 2 }{ 3 }} }{ 3^{\frac{ 2 }{ 3 }} }\]

Answer 7

yes

Answer 8

\[-\frac{ (2^3)^{\frac{ 2 }{ 3 }} }{ \sqrt[3]{3^2} }\]

Answer 9

\[-\frac{ 4 }{ \sqrt[3]{9} }\]

Answer 10

now you can rationalize denominator

Answer 11

How to rationalize denominator?

Answer 12

you have cube root of 3*3. if you have another cube root of 3 then you can rationalize denominator

Answer 13

a number is rationalized when u remove the square root, cube root,.... of it

Answer 14

\[-\frac{ 4 }{ 3\times3 }\] it's like this?

Answer 15

no

Answer 16

\(\Large -\frac{ 4 }{ \sqrt[3]{9} }=-\frac{ 4 }{ \sqrt[3]{9} }\times \frac{\sqrt[3]{9}}{ \sqrt[3]{9} }\\
\Large =-\frac{ 4 \sqrt[3]{9}}{9}\)

Answer 17

\[=\frac{ 4 }{ 9 }\]

Answer 18

i m feeling i made mistake

Answer 19

assuming we're interested only in real roots :

\[\begin{align}\left(-\frac{ 3 }{ 8 }\right)^{-\frac{ 2 }{ 3 }} &= \left(-\frac{ 8 }{ 3 }\right)^{\frac{ 2 }{ 3 }}\\~\\
&= {\left[\left(-\frac{ 8 }{ 3 }\right)^2\right]}^{\frac{ 1 }{ 3 }}\\~\\
&= {\left[\frac{8^2}{3^2}\right]}^{\frac{ 1 }{ 3 }}\\~\\
&= {\left[\frac{(2^3)^2}{3^2}\right]}^{\frac{ 1 }{ 3 }}\\~\\
&= {\left[\frac{2^6}{3^2}\right]}^{\frac{ 1 }{ 3 }}\\~\\
&= {\left[\frac{2^6\times 3}{3^2\times 3}\right]}^{\frac{ 1 }{ 3 }}\\~\\
&= {\left[\frac{2^6\times 3}{3^3}\right]}^{\frac{ 1 }{ 3 }}\\~\\
&= \frac{(2^6\times 3)^{\frac{1}{3}}}{(3^3)^{\frac{1}{3}}}\\~\\
&=\frac{(2^6)^{\frac{1}{3}}3^{\frac{1}{3}}}{3}\\~\\
&=\frac{2^2\sqrt[3]{3}}{3}\\~\\
&= \frac{4\sqrt[3]{3}}{3}
\end{align}\]

Answer 20

The answer in the book say it's 4/9.

Answer 21

lets ask wolfram
http://www.wolframalpha.com/input/?i=simplify+%28-%5Cfrac%7B+3+%7D%7B+8+%7D%29%5E%7B-%5Cfrac%7B+2%7D%7B+3+%7D%7D

Answer 22

hmm

Answer 23

i agree o ganesh

Answer 24

i cant see any trick over there :O

Answer 25

like is it only dealing with reals or what :O

Answer 26

Thnx @ganeshie8 @perl @mathmath333 @ikram002p