Advertisements
Advertisements
प्रश्न
Show that:
`[{x^(a(a-b))/x^(a(a+b))}div{x^(b(b-a))/x^(b(b+a))}]^(a+b)=1`
Advertisements
उत्तर
`[{x^(a(a-b))/x^(a(a+b))}div{x^(b(b-a))/x^(b(b+a))}]^(a+b)=1`
LHS = `[{x^(a(a-b))/x^(a(a+b))}div{x^(b(b-a))/x^(b(b+a))}]^(a+b)`
`=[{x^(a(a-b))/x^(a(a+b))}xx{x^(b(b+a))/x^(b(b-a))}]^(a+b)`
`=[{x^(a^2-ab)/x^(a^2+ab)}xx{x^(b^2+ab)/x^(b^2-ab)}]^(a+b)`
`=[{x^(a^2-ab-a^2-ab)}xx{x^(b^2+ab-b^2+ab)}]^(a+b)`
`=[x^(-2ab)xx x^(2ab)]^(a+b)`
`=[x^(-2ab+2ab)]^(a+b)`
`=[x^0]^(a+b)`
= 1
= RHS
APPEARS IN
संबंधित प्रश्न
Simplify:
`(16^(-1/5))^(5/2)`
Simplify:
`(sqrt2/5)^8div(sqrt2/5)^13`
Prove that:
`(3^-3xx6^2xxsqrt98)/(5^2xxroot3(1/25)xx(15)^(-4/3)xx3^(1/3))=28sqrt2`
Prove that:
`((0.6)^0-(0.1)^-1)/((3/8)^-1(3/2)^3+((-1)/3)^-1)=(-3)/2`
If `a=x^(m+n)y^l, b=x^(n+l)y^m` and `c=x^(l+m)y^n,` Prove that `a^(m-n)b^(n-l)c^(l-m)=1`
Write the value of \[\sqrt[3]{125 \times 27}\].
If \[\sqrt{2} = 1 . 4142\] then \[\sqrt{\frac{\sqrt{2} - 1}{\sqrt{2} + 1}}\] is equal to
Find:-
`32^(1/5)`
Find:-
`32^(2/5)`
Simplify:-
`(1/3^3)^7`
