# How do you simplify #\frac { \root[ 3] { x ^ { 2} y ^ { 7} } } { \root [ 6] { x y ^ { 2} } }#?

By signing up, you agree to our Terms of Service and Privacy Policy

Another approach is to put all the terms under the same root

By signing up, you agree to our Terms of Service and Privacy Policy

Given:

Note that:

where:

Then:

By signing up, you agree to our Terms of Service and Privacy Policy

To simplify the expression (\frac{\sqrt[3]{x^2y^7}}{\sqrt[6]{xy^2}}), we can use the properties of radicals.

First, rewrite the expression using fractional exponents:

(\frac{x^{\frac{2}{3}}y^{\frac{7}{3}}}{x^{\frac{1}{6}}y^{\frac{1}{3}}})

Next, apply the quotient rule for exponents, which states that when dividing like bases, you subtract the exponents:

(x^{\frac{2}{3} - \frac{1}{6}}y^{\frac{7}{3} - \frac{1}{3}})

Simplify the exponents:

(x^{\frac{4}{6}}y^{\frac{6}{6}})

(x^{\frac{2}{3}}y^1)

Finally, rewrite in radical form:

(\sqrt[3]{x^2} \cdot y)

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7