Question

Simplify (3√8)^-1/2​

Answer 1

Answer:

The result after simplification is $\frac{1}{\sqrt{2} }$.

Step-by-step explanation:

It is given that $(\sqrt[3]{8}) ^{-\frac{1}{2} }$

We need to simplify it.

We are given third root of $8$ in this question.

Here, we need to find the third root first and then solve the exponent.

Third root implies the number which is obtained by multiplying the number three times.

Here

$8=2*2*2$

$\sqrt[3]{2*2*2}$

As per definition of cube root.

$=2$

Equation becomes

$(2) ^{-\frac{1}{2} }$

$=(\frac{1}{2} )^{\frac{1}{2} }$

$=\frac{1}{\sqrt{2} }$

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Answer 2

Concept

a number raised to a negative power can be written as the original number's reciprocal to the power in positive. For example- a^-1 = 1/a or more generally, a^(-x) = 1/(a^x).

Given

an expression (3√8)^-1/2​

Find

we need to simplify the given expression

Solution

We have

(3√8)^-1/2​

8 can be written as 2*2*2 or 2^3

thus,

(3√8)^-1/2​ = (3√2^3)^-1/2​

Now cube root of 2 cube will be 2 only, that is, 3√2^3 = (2^3)^1/3 = 2

Thus, the expression becomes

(3√2^3)^-1/2​ = 2^-1/2

2^-1/2 can also be written as

(1/2)^1/2   (as  a^(-x) = 1/(a^x))

= $\frac{1}{\sqrt{2} }$

Thus, on simplifying, the value of (3√8)^-1/2​ becomes $\frac{1}{\sqrt{2} }$

#SPJ3