# College Algebra - Simplify Radical Expression

by Sasha
(Evansville, IN, US)

how to simplify cubed root of 3x^2 divided by the cubed root of 24x^5

### Comments for College Algebra - Simplify Radical Expression

 Sep 07, 2011 Simplify Radical Expression by: Staff The question: by Sasha (Evansville, IN, US) how to simplify cubed root of 3x^2 divided by the cubed root of 24x^5 The answer: 3x^2 divided by the cubed root of 24x^5 [∛(3x²)]/[∛(24x⁵)] You can use either the law of exponents or the distributive law to simplify this expression. Using the distributive law for radicals, you can combine both the numerator and denominator under a single radical sign [∛(3x²)]/[∛(24x⁵)] = ∛[(3x²)/(24x⁵)] You now have a single fraction under a single radial sign. Since you are able to cancel factors which appear in the numerator and denominator of any fraction, you can cancel common factors for this fraction as well. = ∛[(3x²)/(24x⁵)] = ∛[(3*x²)/(3*8*x²*x³)] = ∛{(3 / 3) * (x² / x²) * [1 / (8*x³)]} = ∛{(1) * (1) * [1 / (8*x³)]} = ∛[1 / (8*x³)] Take the cube root of the expression which remains = ∛[1 / (8*x³)] = ∛[1 / (2³*x³)] Using the distributive law for radicals again, you can separate the radical which applies to the numerator from the radical which applies to the denominator. = ∛[1 / (2³*x³)] = ∛(1) / ∛(2³*x³)] Take the cube root of the numerator = ∛(1) / ∛(2³*x³)] = 1 / ∛(2³*x³)] Take the cube root of the denominator = 1 / ∛(2³*x³)] = 1 / (2*x) = 1 / (2x) The final answer is: 1 / (2x) Thanks for writing. Staff www.solving-math-problems.com

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