Advertisements
Advertisements
Question
Prove that:
`((0.6)^0-(0.1)^-1)/((3/8)^-1(3/2)^3+((-1)/3)^-1)=(-3)/2`
Advertisements
Solution
We have to prove that `((0.6)^0-(0.1)^-1)/((3/8)^-1(3/2)^3+((-1)/3)^-1)=(-3)/2`
Let x = `((0.6)^0-(0.1)^-1)/((3/8)^-1(3/2)^3+((-1)/3)^-1)`
`=(1-((0.1xx10)/(1xx10))^-1)/((3^-1/2^(3xx(-1)))(3^3/2^3)+((-1)^-1/3^-1))`
`=(1-1/10^-1)/((3^-1/2^-3)(3^3/2^3)+((-1)/(1/3^1)))`
`=(1-1/(1/10))/((3^(-1+3)/2^(-3+3))+(-1xx3/1))`
`=(1-1xx10)/(3^2/2^0+(-3))`
`=(1-10)/(3^2/1-3)`
`=(-9)/(9-3)`
`=(-9)/6`
`=(-3)/2`
Hence, `((0.6)^0-(0.1)^-1)/((3/8)^-1(3/2)^3+((-1)/3)^-1)=(-3)/2`
APPEARS IN
RELATED QUESTIONS
Simplify the following
`((4xx10^7)(6xx10^-5))/(8xx10^4)`
Prove that:
`(a^-1+b^-1)^-1=(ab)/(a+b)`
Simplify the following:
`(5^(n+3)-6xx5^(n+1))/(9xx5^x-2^2xx5^n)`
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrt(x^-3))^5`
Assuming that x, y, z are positive real numbers, simplify the following:
`(x^-4/y^-10)^(5/4)`
If ax = by = cz and b2 = ac, show that `y=(2zx)/(z+x)`
Solve the following equation:
`4^(2x)=(root3 16)^(-6/y)=(sqrt8)^2`
When simplified \[( x^{- 1} + y^{- 1} )^{- 1}\] is equal to
If 102y = 25, then 10-y equals
Simplify:
`(1^3 + 2^3 + 3^3)^(1/2)`
