Video: Simplifying Rational Numerical Expressions Using the Properties of Operations on Roots

Express 6∛1944/7∛72 in its simplest form.

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Video Transcript

Express six times the cube root of 1944 divided by seven times the cube root of 72 in its simplest form.

The cube root of 𝑎 divided by the cube root of 𝑏 can be rewritten as the cube root of 𝑎 divided by 𝑏. So before we use this property, we can go ahead and separate the fraction of six-sevenths from the cube roots.

Now we can rewrite the cube root part. So we can combine it to be the cube root of one fraction, and then our fraction simplified is actually 27.

And 27 can be written as three cubed. And when you cube root something cubed, it disappears. So we have six-sevenths times three or three over one. So we take six times three divided by seven times one, so our final answer be eighteen-sevenths.

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