Advertisements
Advertisements
Question
Prove that:
`(3^-3xx6^2xxsqrt98)/(5^2xxroot3(1/25)xx(15)^(-4/3)xx3^(1/3))=28sqrt2`
Advertisements
Solution
We have to prove that `(3^-3xx6^2xxsqrt98)/(5^2xxroot3(1/25)xx(15)^(-4/3)xx3^(1/3))=28sqrt2`
Let x = `(3^-3xx6^2xxsqrt98)/(5^2xxroot3(1/25)xx(15)^(-4/3)xx3^(1/3))`
`=(3^-3xx3^2xx2^2xxsqrt(7xx7xx2))/(5^2xxroot3(1/25)xx(15)^-(4/3)xx3^(1/3))`
`=(3^(-3+2)xx2^2xx7sqrt2)/(5^2xx1/5^(2xx1/3)xx5^(-4/3)xx3^(-4/3)xx3^(1/3))`
`=(3^-1xx2^2xx7sqrt2)/(5^2/1xx1/5^(2/3)xx1/5^(4/3)xx1/3^(4/3)xx3^(1/3)/1)`
`=3^-1xx2^2xx7sqrt2xx1/5^2xx5^(2/3)xx5^(4/3)xx3^(4/3)xx1/3^(1/3)`
`=3^-1xx3^(4/3)xx1/3^(1/3)xx4xx7sqrt2xx1/5^2xx5^(2/3)xx5^(4/3)`
`=3^(-1+4/3-1/3)xx4xx7sqrt2xx5^(-2+2/3+4/3)`
`=3^((-1xx3)/(1xx3)+4/3-1/3)xx28sqrt2xx5^((-2xx3)/(1xx3)+2/3+4/3)`
`=3^((-3+4-1)/3)xx28sqrt2xx5^((-6+2+4)/3)`
`=3^0xx28sqrt2xx5^0`
`=1xx28sqrt2xx1`
`=28sqrt2`
Hence, `(3^-3xx6^2xxsqrt98)/(5^2xxroot3(1/25)xx(15)^(-4/3)xx3^(1/3))=28sqrt2`
APPEARS IN
RELATED QUESTIONS
Simplify the following
`(4ab^2(-5ab^3))/(10a^2b^2)`
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrtx)^((-2)/3)sqrt(y^4)divsqrt(xy^((-1)/2))`
Simplify:
`root3((343)^-2)`
Find the value of x in the following:
`5^(2x+3)=1`
State the quotient law of exponents.
If 9x+2 = 240 + 9x, then x =
The simplest rationalising factor of \[\sqrt{3} + \sqrt{5}\] is ______.
The value of \[\sqrt{5 + 2\sqrt{6}}\] is
Find:-
`32^(1/5)`
Find:-
`32^(2/5)`
