Advertisements
Advertisements
प्रश्न
Simplify:
`(sqrt2/5)^8div(sqrt2/5)^13`
Advertisements
उत्तर
Given `(sqrt2/5)^8div(sqrt2/5)^13`
`(sqrt2/5)^8div(sqrt2/5)^13=(2^(1/2xx8)/5^8)div(2^(1/2xx13)/5^13)`
`=(2^4/5^8)div(2^(13/2)/5^13)`
`=(2^4/5^8)/(2^(13/2)/5^13)`
`=(2^4/5^8)xx(5^13/2^(13/2))`
`=(5^13/5^8)xx(2^4/2^(13/2))`
By using the law of rational exponents `a^m/a^n=a^(m-n)`
`rArr(sqrt2/5)^8div(sqrt2/5)^13=5^(13-8)xx2^(4-13/2)`
`rArr(sqrt2/5)^8div(sqrt2/5)^13=5^5xx2^((4xx2)/(1xx2)-13/2)`
`=5^5xx2^(-5/2)`
`=5^5/2^(5/2)`
`=5^5/root2(2xx2xx2xx2xx2)`
`=5^5/(4sqrt2)`
Hence the value of `(sqrt2/5)^8div(sqrt2/5)^13` is `5^5/(4sqrt2)`
APPEARS IN
संबंधित प्रश्न
Simplify the following:
`(3^nxx9^(n+1))/(3^(n-1)xx9^(n-1))`
Solve the following equation for x:
`4^(x-1)xx(0.5)^(3-2x)=(1/8)^x`
Solve the following equations for x:
`2^(2x)-2^(x+3)+2^4=0`
If 2x = 3y = 6-z, show that `1/x+1/y+1/z=0`
If a and b are different positive primes such that
`((a^-1b^2)/(a^2b^-4))^7div((a^3b^-5)/(a^-2b^3))=a^xb^y,` find x and y.
Which one of the following is not equal to \[\left( \sqrt[3]{8} \right)^{- 1/2} ?\]
If x = 2 and y = 4, then \[\left( \frac{x}{y} \right)^{x - y} + \left( \frac{y}{x} \right)^{y - x} =\]
The value of \[\sqrt{3 - 2\sqrt{2}}\] is
Find:-
`125^((-1)/3)`
Simplify:
`7^(1/2) . 8^(1/2)`
