Advertisements
Advertisements
Question
Prove that:
`sqrt(3xx5^-3)divroot3(3^-1)sqrt5xxroot6(3xx5^6)=3/5`
Advertisements
Solution
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
RELATED QUESTIONS
Prove that:
`(x^a/x^b)^cxx(x^b/x^c)^axx(x^c/x^a)^b=1`
Solve the following equation for x:
`4^(x-1)xx(0.5)^(3-2x)=(1/8)^x`
Show that:
`[{x^(a(a-b))/x^(a(a+b))}div{x^(b(b-a))/x^(b(b+a))}]^(a+b)=1`
If 3x = 5y = (75)z, show that `z=(xy)/(2x+y)`
If `27^x=9/3^x,` find x.
Find the value of x in the following:
`2^(x-7)xx5^(x-4)=1250`
Find the value of x in the following:
`(root3 4)^(2x+1/2)=1/32`
If a and b are distinct primes such that `root3 (a^6b^-4)=a^xb^(2y),` find x and y.
If g = `t^(2/3) + 4t^(-1/2)`, what is the value of g when t = 64?
Simplify:
`11^(1/2)/11^(1/4)`
