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
`(4ab^2(-5ab^3))/(10a^2b^2)`
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^(x+1)=4^(x-3)`
Solve the following equations for x:
`3^(2x+4)+1=2.3^(x+2)`
Find the value of x in the following:
`(2^3)^4=(2^2)^x`
If `3^(x+1)=9^(x-2),` find the value of `2^(1+x)`
Solve the following equation:
`sqrt(a/b)=(b/a)^(1-2x),` where a and b are distinct primes.
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 \[\frac{3^{2x - 8}}{225} = \frac{5^3}{5^x},\] then x =
