How do you simplify #(2sqrtx*sqrt(x^3))/sqrt(9x^10)#?

1 Answer
Jan 16, 2018

Answer:

See a solution process below:

Explanation:

First, we can take the square root of the term in the denominator giving:

#(2sqrt(x) * sqrt(x^3))/(3x^5)#

Next, we can use this rule of radicals to simplify the numerator:

#sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))#

#(2sqrt(color(red)(x)) * sqrt(color(blue)(x^3)))/(3x^5) => (2sqrt(color(red)(x) * color(blue)(x^3)))/(3x^5) => (2sqrt(color(red)(x^1) * color(blue)(x^3)))/(3x^5) => (2sqrt(x^(color(red)(1)+color(blue)(3))))/(3x^5) => #

#(2sqrt(x^4))/(3x^5) => (2x^2)/(3x^5)#

We can now use this rule for exponents to simplify the #x# terms:

#x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))#

#(2x^color(red)(2))/(3x^color(blue)(5)) => 2/(3x^(color(blue)(5)-color(red)(2))) => 2/(3x^3)#