Question

If​ ​x​ ​=​ ​8,​ ​y​ ​=​ ​27,​ ​the​ ​value​ ​of​ ​(x4/3+y2/3)1/2​ ​is:

Answer 1

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$(x {}^{ \frac{4}{3} } + y {}^{ \frac{2}{3} } ) {}^{ \frac{1}{2} } \\ put \: the \: value \: of \: x \: and \: y \\ = (8 {}^{ \frac{4}{3} } + 27 {}^{ \frac{2}{3} } ) {}^{ \frac{1}{2} } \\ = (2 {}^{3 \times \frac{4}{3} } + 3 {}^{3 \times \frac{2}{3} } ) {}^{ \frac{1}{2} } \\ = (2 {}^{4} + 3 {}^{2} ) {}^{ \frac{1}{2} } \\ = (16 + 9) {}^{ \frac{1}{2} } \\ = (25) {}^{ \frac{1}{2} } \\ = 5 {}^{2 \times \frac{1}{2} } \\ = 5$
Hope it helps you

Answer 2

Concept

The square root of a number, say x, can also be represented as x^1/2.

Given

​x​ ​=​ ​8 and​ ​y​ ​=​ ​27

Find

we need to find the value of (x^4/3+y^2/3)^1/2​

Solution

We have

x​ ​=​ ​8, and ​y​ ​=​ ​27

substituting the values of x and y in (x^4/3+y^2/3)^1/2​, we will get

(8^4/3+27^2/3)^1/2

8 can be written as 2^3 while 27 can be written as 3^3

thus, the expression becomes

(2^4 + 3^2)^1/2

now 2^4 = 2*2*2*2 =16

and 3^2 = 3*3 =9

thus,

(2^4 + 3^2)^1/2 = (16 + 9)^1/2

= 25^1/2

the square root of 25 is 5,

⇒ 25^1/2 = 5

Thus, If​ ​x​ ​=​ ​8,​ ​y​ ​=​ ​27,​ ​the​ ​value​ ​of​ ​(x^4/3 + y^2/3)^1/2​ ​is 5.

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