Advertisements
Advertisements
प्रश्न
Prove that:
`sqrt(3xx5^-3)divroot3(3^-1)sqrt5xxroot6(3xx5^6)=3/5`
Advertisements
उत्तर
we have to prove that `sqrt(3xx5^-3)/(root3(3^-1)sqrt5)xxroot6(3xx5^6)=3/5`
By using rational exponents `a^-n=1/a^n` we get,
`sqrt(3xx5^-3)/(root3(3^-1)sqrt5)xxroot6(3xx5^6)=sqrt(3xx1/5^3)/(root3(1/3)sqrt5)xxroot6(3xx5^6)`
`=(3^(1/2)xx1/5^(3xx1/2))/(1/3^(1/3)xx5^(1/2))xx3^(1/6)xx5^(6xx1/6)`
`=(3^(1/2)/5^(3/2))/(5^(1/2)/3^(1/3))xx3^(1/6)xx5^1`
`=3^(1/2)/5^(3/2)xx3^(1/3)/5^(1/2)xx3^(1/6)xx5^1`
`=3^(1/2)xx3^(1/3)xx5^(-3/2)xx5^(-1/2)xx3^(1/6)xx5^1`
`=3^(1/2+1/3+1/6)xx5^(-3/2-1/2+1)`
`=3^((1xx3)/(2xx3)+(1xx2)/(3xx2)+1/6)xx5^(-3/2-1/2+(1xx2)/(1xx2))`
`=3^((3+2+1)/6)xx5^((-3-1+2)/2)`
`=3^1xx5^-1`
`=3xx1/5`
`=3/5`
Hence `sqrt(3xx5^-3)/(root3(3^-1)sqrt5)xxroot6(3xx5^6)=3/5`
APPEARS IN
संबंधित प्रश्न
Simplify the following
`(4ab^2(-5ab^3))/(10a^2b^2)`
If a = 3 and b = -2, find the values of :
ab + ba
Solve the following equation for x:
`2^(x+1)=4^(x-3)`
Find the value of x in the following:
`2^(x-7)xx5^(x-4)=1250`
Find the value of x in the following:
`(13)^(sqrtx)=4^4-3^4-6`
If `5^(3x)=125` and `10^y=0.001,` find x and y.
If a and b are distinct primes such that `root3 (a^6b^-4)=a^xb^(2y),` find x and y.
Simplify:
`(x^(a+b)/x^c)^(a-b)(x^(b+c)/x^a)^(b-c)(x^(c+a)/x^b)^(c-a)`
If `x = a^(m + n), y = a^(n + l)` and `z = a^(l + m),` prove that `x^my^nz^l = x^ny^lz^m`
If \[\sqrt{2^n} = 1024,\] then \[{3^2}^\left( \frac{n}{4} - 4 \right) =\]
