Answered

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Which expression is equivalent to

( 4^(1/3) × 4^(2/6) ) ^(3/4)
( ---------÷------------ )
( 4^(5/6) )

*All the numbers in the division problem are in parenthesis with the ^(3/4) on the outside.*

A: (1/4)^(3/66)
B: (1/4)^(-3/66)
C:(1/4)^(-1/11)
D: (1/4)^(1/11)

Sagot :

abidemiokin

The simplified form of the expression is [tex]4^{-1/3}[/tex]

Indices and exponents

Given the indices expression as shown;
[tex]\frac{(4^{1/3}\times 4^{2/6} )^{3/4}}{4^{5/6}}[/tex]

Applying the product and quotient law of indices

[tex]\frac{(4^{1/3+1/3})^{3/4}}{4^{5/6}}\\\frac{(4^{2/3})^{3/4}}{4^{5/6}}\\\frac{4^{1/2}}{4^{5/6}}\\[/tex]

Take the difference in the power to have:

4^(1/2 - 5/6)

4^(-2/6)

[tex]4^{-1/3}[/tex]

Hence the simplified form of the expression is [tex]4^{-1/3}[/tex]

Learn more on indices here: https://brainly.com/question/10339517

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