Question

The simplified value of (81)^–1/4 × ⁴√81 × (81)^0.2 is
(a) 9
(b) 3
(c) 1
(d) 0
​

Answer 1

Answer:

I think the last exponent should be 0.5 then the answer will be (a) 9

Step-by-step explanation:

(81)^-1/4* (81)^1/4*(81)^0.5

(81)^(-14+1/4+0.5) as base is equal we can add the exponent

(81)^0.5 as -1/4 and 1/4 in the power gets canceled on addition

(sqrt 81) = 9

Answer 2

Given:

(81)^–1/4 × ⁴√81 × (81)^0.25

To Find:

The simplified value is

(a) 9

(b) 3

(c) 1

(d) 0

Solution:

Before proceeding with this question let's have some basic ideas about some basics of exponential. Any number to the negative power is the inverse of that number to the positive of that power and any number to power to the whole power then the powers are multiplied together.

Now simplifying the expression,

$=81^{-\frac{1}{4}}*\sqrt[4]{81}*81^{0.25}$

Here we will need to inverse the negative power of 81 and also express0.25 as 1/4 which will be the 4th root and we can solve it by finding the 4th root or using the powers.

$=81^{-\frac{1}{4}}*\sqrt[4]{81}*81^{0.25}\\=\frac{1}{81^{\frac{1}{4} }}*81^{\frac{1}{4}}*81^{\frac{1}{4} } \\= \frac{1}{(3^4)^{\frac{1}{4} }}*(3^4)^{\frac{1}{4}}*(3^4)^{\frac{1}{4} }$

Now every power will cancel it each other or will be equal to 1 then the following expression can now be expressed as

$=\frac{1}{3} *3*3\\=3$

Hence, the correct option will be (b).

Right Question:

The simplified value of (81)^–1/4 × ⁴√81 × (81)^0.25 is

(a) 9

(b) 3

(c) 1

(d) 0