Advertisements
Advertisements
Question
Simplify:
`(x^(a+b)/x^c)^(a-b)(x^(b+c)/x^a)^(b-c)(x^(c+a)/x^b)^(c-a)`
Advertisements
Solution
`(x^(a+b)/x^c)^(a-b)(x^(b+c)/x^a)^(b-c)(x^(c+a)/x^b)^(c-a)`
`=(x^((a+b)(a-b))/x^(c(a-b)))(x^((b+c)(b-c))/x^(a(b-c)))(x^((c+a)(c-a))/x^(b(c-a)))`
`=(x^(a^2-b^2)/x^(ca-bc))(x^(b^2-c^2)/x^(ab-ac))(x^(c^2-a^2)/x^(bc-ab))`
`=x^(a^2-b^2+b^2-c^2+c^2-a^2)/x^(ca-bc+ab-ac+bc-ab)`
`=x^0/x^0`
= 1
APPEARS IN
RELATED QUESTIONS
Simplify the following
`(a^(3n-9))^6/(a^(2n-4))`
Prove that:
`(a^-1+b^-1)^-1=(ab)/(a+b)`
Simplify the following:
`(6(8)^(n+1)+16(2)^(3n-2))/(10(2)^(3n+1)-7(8)^n)`
Solve the following equation for x:
`2^(3x-7)=256`
Simplify:
`(sqrt2/5)^8div(sqrt2/5)^13`
Prove that:
`(2^n+2^(n-1))/(2^(n+1)-2^n)=3/2`
The simplest rationalising factor of \[2\sqrt{5}-\]\[\sqrt{3}\] is
If \[x = 7 + 4\sqrt{3}\] and xy =1, then \[\frac{1}{x^2} + \frac{1}{y^2} =\]
If \[\sqrt{2} = 1 . 4142\] then \[\sqrt{\frac{\sqrt{2} - 1}{\sqrt{2} + 1}}\] is equal to
Simplify:-
`(1/3^3)^7`
