Question

http://prntscr.com/9423gt

Answer 1

@ganeshie8

Answer 2

@Jhannybean

Answer 3

When you have indices to the power, you multiply those indices. This is one of the indice laws which states:

\[(x^y )^z = x^{yz}\]

When you take a number to the power of a negative number, you "turn it upside down" in order to convert the negative power into a positive one, like so:

\[x^{-4} = \frac{ 1 }{ x^4 }\]

Take the equation bit by bit.

\[(\frac{ 1 }{4 } a^2b^{-3})^{-1/4}\]

=

\[(\frac{ 1 }{ 4 }^{-1/4} ) *(a^2)^{-1/4} *(b^{-3})^{-1/4} \]

=

\[(\frac{ 4 }{ 1 })^{1/4} *(a^{-\frac{ 1 }{ 2 }}) * (b ^{3/4})\]

=

\[\frac{ \sqrt2* b^{3/4} }{ a^{1/2}}\]

The reason we have \[\sqrt2\] is because \[4^{1/4} = 2^{1/2} = \sqrt2 \] - (Any number to the power is half is squared)

therefore the answer is D.

Answer 4

thnx