How do you simplify (9 sqrt(50x^2)) / (3 sqrt(2x^4))?

1 Answer
Johnson Z.
Apr 14, 2016

15/x

Explanation:

1. Start by factoring out 3 from the numerator and denominator.

(9sqrt(50x^2))/(3(sqrt(2x^4))

=(3(3sqrt(50x^2)))/(3(sqrt(2x^4)))

=(3sqrt(50x^2))/(sqrt(2x^4))

2. Multiply the numerator and denominator by sqrt(2x^4) to get rid of the radical in the denominator.

=(3sqrt(50x^2))/(sqrt(2x^4))((sqrt(2x^4))/(sqrt(2x^4)))

3. Simplify.

=(3sqrt(100x^6))/(2x^4)

=(3*10sqrt(x^6))/(2x^4)

=(3*5x^(6(1/2)))/x^4

=(15x^3)/x^4

3. Use the exponent quotient law, color(purple)b^color(red)m-:color(purple)b^color(blue)n=color(purple)b^(color(red)m-color(blue)n), to simplify x^3/x^4.

=15x^(3-4)

=15x^-1

=color(green)(|bar(ul(color(white)(a/a)15/xcolor(white)(a/a)|)))

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