Advertisements
Advertisements
प्रश्न
Simplify:
`root(lm)(x^l/x^m)xxroot(mn)(x^m/x^n)xxroot(nl)(x^n/x^l)`
Advertisements
उत्तर
`root(lm)(x^l/x^m)xxroot(mn)(x^m/x^n)xxroot(nl)(x^n/x^l)`
`=(x^l/x^m)^(1/(lm))xx(x^m/x^n)^(1/(mn))xx(x^n/x^l)^(1/(nl))`
`=(x^(l-m))^(1/ml)xx(x^(m-n))^(1/mn)xx(x^(n-l))^(1/)nl`
`=x^((l-m)/(ml))xx x^((m-n)/(mn))xx x^((n-l)/(nl))`
`=x^((l-m)/(ml)+(m-n)/(mn)+(n-l)/(nl))`
`=x^((ln-mn+lm-nl+nm-lm)/(nml))`
`=x^0`
= 1
APPEARS IN
संबंधित प्रश्न
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrt2/sqrt3)^5(6/7)^2`
Show that:
`1/(1+x^(a-b))+1/(1+x^(b-a))=1`
Show that:
`(a^(x+1)/a^(y+1))^(x+y)(a^(y+2)/a^(z+2))^(y+z)(a^(z+3)/a^(x+3))^(z+x)=1`
For any positive real number x, find the value of \[\left( \frac{x^a}{x^b} \right)^{a + b} \times \left( \frac{x^b}{x^c} \right)^{b + c} \times \left( \frac{x^c}{x^a} \right)^{c + a}\].
If a, b, c are positive real numbers, then \[\sqrt{a^{- 1} b} \times \sqrt{b^{- 1} c} \times \sqrt{c^{- 1} a}\] is equal to
If (16)2x+3 =(64)x+3, then 42x-2 =
The simplest rationalising factor of \[\sqrt[3]{500}\] is
If x = \[\frac{2}{3 + \sqrt{7}}\],then (x−3)2 =
If \[x = 7 + 4\sqrt{3}\] and xy =1, then \[\frac{1}{x^2} + \frac{1}{y^2} =\]
Find:-
`125^(1/3)`
