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
`((4xx10^7)(6xx10^-5))/(8xx10^4)`
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrt(x^-3))^5`
Show that:
`{(x^(a-a^-1))^(1/(a-1))}^(a/(a+1))=x`
Solve the following equation:
`4^(x-1)xx(0.5)^(3-2x)=(1/8)^x`
Simplify:
`root(lm)(x^l/x^m)xxroot(mn)(x^m/x^n)xxroot(nl)(x^n/x^l)`
Write the value of \[\sqrt[3]{7} \times \sqrt[3]{49} .\]
Which of the following is (are) not equal to \[\left\{ \left( \frac{5}{6} \right)^{1/5} \right\}^{- 1/6}\] ?
If x = 2 and y = 4, then \[\left( \frac{x}{y} \right)^{x - y} + \left( \frac{y}{x} \right)^{y - x} =\]
If \[\sqrt{2^n} = 1024,\] then \[{3^2}^\left( \frac{n}{4} - 4 \right) =\]
The value of \[\sqrt{5 + 2\sqrt{6}}\] is
