Advertisements
Advertisements
प्रश्न
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrtx)^((-2)/3)sqrt(y^4)divsqrt(xy^((-1)/2))`
Advertisements
उत्तर
We have to simplify the following, assuming that x, y, z are positive real numbers
Given `(sqrtx)^((-2)/3)sqrt(y^4)divsqrt(xy^((-1)/2))`
`=(x^(1/2))^(-2/3)(y^4)^(1/2)div(x xxy^(-1/2))^(1/2)`
`=(x^(1/2xx-2/3)xxy^(4xx1/2))/(x^(1/2)xxy^(-1/2xx1/2))`
`=(x^(-1/3)xxy^2)/(x^(1/2)xxy^(-1/4))`
By using the law of rational exponents, `a^mdiva^n=a^(m-n)` we have
`=x^(-1/3-1/2)xxy^(2+1/4)`
`=x^(-5/6)xxy^(9/4)`
`=1/x^(5/6)xxy^(9/4)`
`=y^(9/4)/x^(5/6)`
APPEARS IN
संबंधित प्रश्न
If abc = 1, show that `1/(1+a+b^-1)+1/(1+b+c^-1)+1/(1+c+a^-1)=1`
If `1176=2^a3^b7^c,` find a, b and c.
Given `4725=3^a5^b7^c,` find
(i) the integral values of a, b and c
(ii) the value of `2^-a3^b7^c`
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrt(x^-3))^5`
Prove that:
`sqrt(3xx5^-3)divroot3(3^-1)sqrt5xxroot6(3xx5^6)=3/5`
Show that:
`(a^(x+1)/a^(y+1))^(x+y)(a^(y+2)/a^(z+2))^(y+z)(a^(z+3)/a^(x+3))^(z+x)=1`
If `x=2^(1/3)+2^(2/3),` Show that x3 - 6x = 6
The value of x − yx-y when x = 2 and y = −2 is
If 10x = 64, what is the value of \[{10}^\frac{x}{2} + 1 ?\]
The simplest rationalising factor of \[2\sqrt{5}-\]\[\sqrt{3}\] is
