Advertisements
Advertisements
प्रश्न
Simplify:
`(x^(a+b)/x^c)^(a-b)(x^(b+c)/x^a)^(b-c)(x^(c+a)/x^b)^(c-a)`
Advertisements
उत्तर
`(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
संबंधित प्रश्न
Find:-
`9^(3/2)`
Simplify the following
`((4xx10^7)(6xx10^-5))/(8xx10^4)`
Solve the following equation for x:
`2^(5x+3)=8^(x+3)`
If 49392 = a4b2c3, find the values of a, b and c, where a, b and c are different positive primes.
Find the value of x in the following:
`(sqrt(3/5))^(x+1)=125/27`
If `3^(4x) = (81)^-1` and `10^(1/y)=0.0001,` find the value of ` 2^(-x+4y)`.
Solve the following equation:
`4^(2x)=(root3 16)^(-6/y)=(sqrt8)^2`
State the power law of exponents.
If a, b, c are positive real numbers, then \[\sqrt[5]{3125 a^{10} b^5 c^{10}}\] is equal to
Find:-
`32^(1/5)`
