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Question
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`
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