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
Prove that:
`(a+b+c)/(a^-1b^-1+b^-1c^-1+c^-1a^-1)=abc`
Prove that:
`((0.6)^0-(0.1)^-1)/((3/8)^-1(3/2)^3+((-1)/3)^-1)=(-3)/2`
Show that:
`1/(1+x^(a-b))+1/(1+x^(b-a))=1`
Show that:
`[{x^(a(a-b))/x^(a(a+b))}div{x^(b(b-a))/x^(b(b+a))}]^(a+b)=1`
Simplify:
`root(lm)(x^l/x^m)xxroot(mn)(x^m/x^n)xxroot(nl)(x^n/x^l)`
If `x = a^(m + n), y = a^(n + l)` and `z = a^(l + m),` prove that `x^my^nz^l = x^ny^lz^m`
Write the value of \[\sqrt[3]{125 \times 27}\].
If a, m, n are positive ingegers, then \[\left\{ \sqrt[m]{\sqrt[n]{a}} \right\}^{mn}\] is equal to
If (16)2x+3 =(64)x+3, then 42x-2 =
If \[\sqrt{13 - a\sqrt{10}} = \sqrt{8} + \sqrt{5}, \text { then a } =\]
