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Write (1/9)^(-1/2)\ xx\ (64)^(-1/3) as a...

Write `(1/9)^(-1/2)\ xx\ (64)^(-1/3)` as a rational number.

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`(1/9)^(−1/2)×(64)^(−1/3)`
`=(1/3)^(2×(-1/2))xx4^(3xx(-1/3))`
`=(1/3)^(-1)×4^(-1)`
`=3xx1/4`
`=3/4`
`therefore (1/9)^(-1/2)\ xx\ (64)^(-1/3)=3/4`
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(64)^(-2/3) xx (1/4)^(-3) equals:

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16/9 xx (-1(1)/2)^(3)=

64^(2/3)xx64^(1/3)xx64^((-5)/3)

Assertion : One of the rational number between (1)/(5) and (1)/(4) is (9)/(2) . Reason : If x and y are any two rational numbers such that x lt y , then (1)/(2)(x+y) is a rational number between x and y such that x lt (1)/(2) (x+y) lt y .

The value of 3xx 9^(-3//2) xx 9^(1//2) is

RD SHARMA-EXPONENTS OF REAL NUMBER-All Questions
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  2. Write the value of root(3)(7)\ xx\root(3)( 49)

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  4. Write the value of root(3)(125)\ xx\ root(3)(27)

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