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Prove that: ((0. 6)^0- (0. 1)^(-1))/((3/...

Prove that: `((0. 6)^0- (0. 1)^(-1))/((3/8)^(-1) (3/2)^3+ (-1/3)^(-1))= -3/2`

Text Solution

Verified by Experts

Given:
`=(1-(1/10)^-1)/((3/8)^(-1)(3/2)^(3)+(-1/3)^(-1))`
Using the property:
`(a/b)^-n=(b/a)^n`
`a^m/a^n=a^m-n`
`(a^m)^n= a^(m xx n)`
`=1-10/(3/3) xx 3^(3)/2^(3)-3`
`=-9/9-3`
`=-9/6`
`=-3/2`
Hence proved.
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Knowledge Check

  • Solve the followings : The value of expression ((0.6)^0 - (0.1)^(-1))/((3/(2^3))^(-1) . (3/2)^(3) + (-1/3)^(-1)) is :

    A
    `-3/2`
    B
    `2/3`
    C
    `3/2`
    D
    `9/4`

  • The value of expression ((0.6)^(0)-(0.1)^(-1))/(((3)/(2^(3)))^(-1).((3)/(2))^(3)+(-(1)/(3))^(-1)) is

    A
    `-3//2`
    B
    `2//3`
    C
    `3//2`
    D
    `9//4`

  • Value of (( 0. 5) ^( 0) - ( 0. 1) ^(-1))/( ( (3)/(4) ) ^( -1) ( (3)/(2)) ^(3) + ((-1)/( 3)) ^( -2)) is

    A
    `3//2`
    B
    `-2//3`
    C
    `-3//2`
    D
    `2//3`

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