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If X-2 = 64, Then X1/3+X0 = - Mathematics

MCQ

If x-2 = 64, then x1/3+x0 =

Options

  • 2

  • 3

  • 3/2

  • 2/3

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Solution

We have to find the value of `x^(1/3+ x^0)` if  `x^-2 = 64`

Consider,

 `x^-2 = 2^6`

 `1/x^2 = 2^6`

Multiply  `1/2`on both sides of powers we get 

`1/x^(2 xx 1/2) = 2^(6x1/2)`

`1/x^(2 xx 1/2) = 2^(6x1/2)`

`1/x = 2^3`

`1/x = 8/ 1`

By taking reciprocal on both sides we get,

 `1/8 = x `

Substituting `1/8` in `x^(1/3 + x^0)`we get

`= (1/8)^(1/3) + (1/8)^0`

`= (1/(2^3))^(1/3) + (1/8)^0`

`= 1/(2^(3xx 1/3)) +1`

` = 1/2^1 + 1` 

`=1/2 +1`

By taking least common multiply we get 

`= 1/2 + (1 xx 2)/(1 xx 2)`

` = 1/2 + 2/2 `

`= (1+2)/2`

`= 3/2`

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 2 Exponents of Real Numbers
Q 10 | Page 30
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