Advertisements
Advertisements
प्रश्न
Prove that:
`(3^-3xx6^2xxsqrt98)/(5^2xxroot3(1/25)xx(15)^(-4/3)xx3^(1/3))=28sqrt2`
Advertisements
उत्तर
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
संबंधित प्रश्न
If a = 3 and b = -2, find the values of :
(a + b)ab
Solve the following equation for x:
`7^(2x+3)=1`
Show that:
`(3^a/3^b)^(a+b)(3^b/3^c)^(b+c)(3^c/3^a)^(c+a)=1`
Find the value of x in the following:
`(3/5)^x(5/3)^(2x)=125/27`
Find the value of x in the following:
`(13)^(sqrtx)=4^4-3^4-6`
If `x = a^(m + n), y = a^(n + l)` and `z = a^(l + m),` prove that `x^my^nz^l = x^ny^lz^m`
If x-2 = 64, then x1/3+x0 =
If a, m, n are positive ingegers, then \[\left\{ \sqrt[m]{\sqrt[n]{a}} \right\}^{mn}\] is equal to
If \[4x - 4 x^{- 1} = 24,\] then (2x)x equals
The simplest rationalising factor of \[\sqrt{3} + \sqrt{5}\] is ______.
