Question

symplify the question (81)-1/4​

Answer 1

81/1 - 1/4

LCM = 4

[(81×4) - (1×1)]/4

[324-1]/4

323/4

80 3/4

Answer 2

Answer:

Given:

to simplify (81)-1/4

Pre-requisite Knowledge

• $a^{-m}=\dfrac{1}{a^m}$

• $3^2=9$
• $9^2=81$
• $3^4=81$

Solving Question:

  to find the answer first we have to simplify 81 then proceed further.

Solution:

$a^{-m}=\dfrac{1}{a^m}\\\\substitute\:the\:value\\\\(81)^{\dfrac{-1}{4}}\\\\\implies (9)^{2*\dfrac{-1}{4}}=(9)^{\dfrac{-1}{2}}\\\\\implies {\sqrt{9}}^{\:-1}\\\\\implies (3)^{-1}\\\\\implies \dfrac{1}{3}$

Thus, the simplified form of $(81)^{\dfrac{-1}{4}}$ is 1/3