Rewrite the radical expression as an exponential expression: $4y\sqrt{x^7}$

Expert intro: To rewrite a radical expression as an exponential expression, keep factors outside the radical and change the radical part into a rational exponent.

Detailed walkthrough

Use the square root rule

$\sqrt{a}=a^{\frac{1}{2}}$

Then

$4y\sqrt{x^7}=4y(x^7)^{\frac{1}{2}}$

You can also combine the exponent:

$4y x^{\frac{7}{2}}$

Both forms are equivalent.

💡 Pitfall guide

Do not change the coefficient $4y$. Only the radical part becomes a fractional exponent. Another common error is writing $x^{7/2}$ without recognizing that it comes from $(x^7)^{1/2}$.

🔄 Real-world variant

If the problem were $4y\sqrt[3]{x^7}$, the exponential form would be $4y(x^7)^{1/3}=4yx^{7/3}$.

🔍 Related terms

square root, fractional exponent, radical expression