Question

simplify (81a4b8c-4)1/4​

Answer 1

SOLUTION

TO EVALUATE

$\displaystyle \sf{ {(81 {a}^{4} {b}^{8} {c}^{ - 4} )}^{ \frac{1}{4} } }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula on indices that

$\displaystyle \sf{ {( {a}^{m} )}^{n} = {a}^{mn} }$

EVALUATION

Here the given expression is

$\displaystyle \sf{ {(81 {a}^{4} {b}^{8} {c}^{ - 4} )}^{ \frac{1}{4} } }$

Now

$\displaystyle \sf{ {81 {a}^{4} {b}^{8} {c}^{ - 4}}^{ } }$

$\displaystyle \sf{ = { {3}^{4} {a}^{4} { ({b}^{2} )}^{4} { ({c}^{ - 1}) }^{4} }^{ } }$

$\displaystyle \sf{ = {(3a {b}^{2} {c}^{ - 1} )}^{4} }$

Now

$\displaystyle \sf{ {(81 {a}^{4} {b}^{8} {c}^{ - 4} )}^{ \frac{1}{4} } }$

$\displaystyle \sf{ = { \bigg( {(3a {b}^{2} {c}^{ - 1} )}^{4} \bigg)}^{ \frac{1}{4} } }$

$\displaystyle \sf{ = { \bigg( {(3a {b}^{2} {c}^{ - 1} )}^{} \bigg)}^{4 \times \frac{1}{4} } }$

$\displaystyle \sf{ = { \bigg( {(3a {b}^{2} {c}^{ - 1} )}^{} \bigg)}^{1 } }$

$\displaystyle \sf{ = 3a {b}^{2} {c}^{ - 1} }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. Using law of exponents, simplify (5²)³÷5³

https://brainly.in/question/36250730

2. If 2x× 4x=(8)1/3 × (32)1/5 ,then find the value of x

https://brainly.in/question/14155738

Answer 2

Answer:

thank you veerryyyy much