Question

I NEED HELP PLEASE !!!!!

Answer 1

Answer:

The answer is

$({ \frac{1}{4} })^{ \frac{3}{66} }$

Step-by-step explanation:

$({ \frac{ {4}^{ \frac{1}{3} }. {4}^{ \frac{2}{6} } }{ {4}^{ \frac{5}{6} } } })^{ \frac{3}{11} }$

First solve the numerator first

Using the rules of indices since the bases are the same and are multiplying we add the exponents

That's

${4}^{ \frac{1}{3} } . {4}^{ \frac{2}{6} } = {4}^{ \frac{1}{3} + \frac{2}{6} } = {4}^{ \frac{2}{3} }$

So we now have

$( \frac{ {4}^{ \frac{2}{3} } }{ {4}^{ \frac{5}{6} } } )^{ \frac{3}{11} }$

Again using the rules of indices since the bases are dividing we subtract the exponents

That's

$\frac{ {4}^{ \frac{2}{3} } }{ {4}^{ \frac{5}{6} } } = {4}^{ \frac{2}{3} - \frac{5}{6} } = {4}^{ - \frac{1}{6} }$

So we now have

$( { {4}^{ - \frac{1}{6} } })^{ \frac{3}{11} }$

Using the rules of indices solve the expression

$( { {a}^{x} })^{y} = {a}^{x \times y}$

That's

$( { {4}^{ - \frac{1}{6} } })^{ \frac{3}{11} } = {4}^{ - \frac{1}{6} \times \frac{3}{11} } = {4}^{ - \frac{3}{66} }$

Again using the rules of indices

That's

${x}^{ - y} = \frac{1}{ {x}^{y} }$

Rewrite the expression

We have the final answer as

$({ \frac{1}{4} })^{ \frac{3}{66} }$

Hope this helps you