Advertisements
Advertisements
Question
Simplify:
`root(lm)(x^l/x^m)xxroot(mn)(x^m/x^n)xxroot(nl)(x^n/x^l)`
Advertisements
Solution
`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
RELATED QUESTIONS
Prove that:
`(x^a/x^b)^(a^2+ab+b^2)xx(x^b/x^c)^(b^2+bc+c^2)xx(x^c/x^a)^(c^2+ca+a^2)=1`
Prove that:
`(x^a/x^b)^cxx(x^b/x^c)^axx(x^c/x^a)^b=1`
Simplify:
`(sqrt2/5)^8div(sqrt2/5)^13`
If 2x = 3y = 6-z, show that `1/x+1/y+1/z=0`
Find the value of x in the following:
`5^(x-2)xx3^(2x-3)=135`
Find the value of x in the following:
`(sqrt(3/5))^(x+1)=125/27`
Solve the following equation:
`3^(x-1)xx5^(2y-3)=225`
Write the value of \[\left\{ 5( 8^{1/3} + {27}^{1/3} )^3 \right\}^{1/4} . \]
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
The positive square root of \[7 + \sqrt{48}\] is
