Advertisements
Advertisements
Question
Assuming that x, y, z are positive real numbers, simplify the following:
`(x^((-2)/3)y^((-1)/2))^2`
Advertisements
Solution
We have to simplify the following, assuming that x, y, z are positive real numbers
Given `(x^((-2)/3)y^((-1)/2))^2`
As x and y are positive real numbers then we have
`(x^((-2)/3)y^((-1)/2))^2=(x^((-2)/3)xxx^((-2)/3)xxy^((-1)/2)xxy^((-1)/2))`
By using law of rational exponents `a^-n=1/a^n` we have
`(x^((-2)/3)y^((-1)/2))^2=1/x^(2/3)xx1/x^(2/3)xx1/y^(1/2)xx1/y^(1/2)`
`(x^((-2)/3)y^((-1)/2))^2=1/(x^(2/3)xx x^(2/3))xx1/(y^(1/2)xxy^(1/2))`
By using law of rational exponents `a^m xx a^n=a^(m+n)` we have
`(x^((-2)/3)y^((-1)/2))^2=1/x^(2/3+2/3)xx1/y^(1/2+1/2)`
`=1/x^(4/3)xx1/y^(2/2)`
`=1/x^(4/3)xx1/y`
`=1/(x^(4/3)y)`
Hence the simplified value of `(x^((-2)/3)y^((-1)/2))^2` is `1/(x^(4/3)y)`
APPEARS IN
RELATED QUESTIONS
Simplify the following
`(4ab^2(-5ab^3))/(10a^2b^2)`
Solve the following equation for x:
`2^(3x-7)=256`
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrt(x^-3))^5`
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrt2/sqrt3)^5(6/7)^2`
Show that:
`(x^(a^2+b^2)/x^(ab))^(a+b)(x^(b^2+c^2)/x^(bc))^(b+c)(x^(c^2+a^2)/x^(ac))^(a+c)=x^(2(a^3+b^3+c^3))`
Find the value of x in the following:
`(sqrt(3/5))^(x+1)=125/27`
Solve the following equation:
`3^(x-1)xx5^(2y-3)=225`
Solve the following equation:
`8^(x+1)=16^(y+2)` and, `(1/2)^(3+x)=(1/4)^(3y)`
The value of \[\left\{ 2 - 3 (2 - 3 )^3 \right\}^3\] is
If 10x = 64, what is the value of \[{10}^\frac{x}{2} + 1 ?\]
