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
If a = 3 and b = -2, find the values of :
ab + ba
Find the value of x in the following:
`(2^3)^4=(2^2)^x`
If 1176 = `2^axx3^bxx7^c,` find the values of a, b and c. Hence, compute the value of `2^axx3^bxx7^-c` as a fraction.
Write \[\left( \frac{1}{9} \right)^{- 1/2} \times (64 )^{- 1/3}\] as a rational number.
For any positive real number x, find the value of \[\left( \frac{x^a}{x^b} \right)^{a + b} \times \left( \frac{x^b}{x^c} \right)^{b + c} \times \left( \frac{x^c}{x^a} \right)^{c + a}\].
The value of x − yx-y when x = 2 and y = −2 is
If \[\sqrt{5^n} = 125\] then `5nsqrt64`=
If \[x = \sqrt{6} + \sqrt{5}\],then \[x^2 + \frac{1}{x^2} - 2 =\]
Which of the following is equal to x?
Simplify:
`(3/5)^4 (8/5)^-12 (32/5)^6`
