Advertisements
Advertisements
Question
Prove that:
`(x^a/x^b)^cxx(x^b/x^c)^axx(x^c/x^a)^b=1`
Advertisements
Solution
Consider the left hand side:
`(x^a/x^b)^cxx(x^b/x^c)^axx(x^c/x^a)^b=1`
`=x^(ac)/x^(bc)xxx^(ba)/x^(ca)xxx^(cb)/x^(ab)`
`=(x^(ac)xxx^(ba)xxx^(cb))/(x^(bc)xxx^(ca)xxx^(ab))`
`=x^(ac+ba+cb)/x^(bc+ca+ab)`
= 1
Left hand side is equal to right hand side.
Hence proved.
APPEARS IN
RELATED QUESTIONS
Find:-
`9^(3/2)`
Simplify the following
`((4xx10^7)(6xx10^-5))/(8xx10^4)`
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrtx)^((-2)/3)sqrt(y^4)divsqrt(xy^((-1)/2))`
Write \[\left( 625 \right)^{- 1/4}\] in decimal form.
State the power law of exponents.
`(2/3)^x (3/2)^(2x)=81/16 `then x =
The value of \[\left\{ 8^{- 4/3} \div 2^{- 2} \right\}^{1/2}\] is
If \[\frac{3^{2x - 8}}{225} = \frac{5^3}{5^x},\] then x =
\[\frac{5^{n + 2} - 6 \times 5^{n + 1}}{13 \times 5^n - 2 \times 5^{n + 1}}\] is equal to
Find:-
`32^(1/5)`
