Advertisements
Advertisements
प्रश्न
Prove that:
`(x^a/x^b)^cxx(x^b/x^c)^axx(x^c/x^a)^b=1`
Advertisements
उत्तर
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
संबंधित प्रश्न
Solve the following equations for x:
`2^(2x)-2^(x+3)+2^4=0`
Assuming that x, y, z are positive real numbers, simplify the following:
`root5(243x^10y^5z^10)`
If 3x = 5y = (75)z, show that `z=(xy)/(2x+y)`
Solve the following equation:
`sqrt(a/b)=(b/a)^(1-2x),` where a and b are distinct primes.
Simplify:
`root(lm)(x^l/x^m)xxroot(mn)(x^m/x^n)xxroot(nl)(x^n/x^l)`
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 \[\sqrt[5]{3125 a^{10} b^5 c^{10}}\] is equal to
(256)0.16 × (256)0.09
If \[\sqrt{2^n} = 1024,\] then \[{3^2}^\left( \frac{n}{4} - 4 \right) =\]
Find:-
`16^(3/4)`
