Advertisements
Advertisements
प्रश्न
Simplify:
`(sqrt2/5)^8div(sqrt2/5)^13`
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
Prove that:
`(x^a/x^b)^cxx(x^b/x^c)^axx(x^c/x^a)^b=1`
Simplify the following:
`(3^nxx9^(n+1))/(3^(n-1)xx9^(n-1))`
Simplify the following:
`(5^(n+3)-6xx5^(n+1))/(9xx5^x-2^2xx5^n)`
If `1176=2^a3^b7^c,` find a, b and c.
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrt(x^-3))^5`
Find the value of x in the following:
`(3/5)^x(5/3)^(2x)=125/27`
If a and b are different positive primes such that
`(a+b)^-1(a^-1+b^-1)=a^xb^y,` find x + y + 2.
For any positive real number x, find the value of \[\left( \frac{x^a}{x^b} \right)^{a + b} \times \left( \frac{x^b}{x^c} \right)^{b + c} \times \left( \frac{x^c}{x^a} \right)^{c + a}\].
Simplify \[\left[ \left\{ \left( 625 \right)^{- 1/2} \right\}^{- 1/4} \right]^2\]
The value of 64-1/3 (641/3-642/3), is
