To convert the given radical expression to its rational exponent form and then simplify

DofotheroU 2021-08-10 Answered
To convert the given radical expression to its rational exponent form and then simplify
image

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

ensojadasH
Answered 2021-08-11 Author has 16275 answers
I hope my answer below will help you
image
Not exactly what you’re looking for?
Ask My Question
9
 
Vasquez
Answered 2021-12-27 Author has 10020 answers

Step 1

Then given expression can be written as:

\(\sqrt[3]{8x^3y^{12}}=(8x^3 y^{12})^{\frac 13} \ \ \ (\text{Since } \sqrt[n]{a}=a^{\frac 1n})\)

\(\sqrt[3]{8x^3y^{12}} (8)^{\frac 13} (x^3)^{\frac 13} (y^{12})^{\frac 13} \ \ \ \ (Since (ab)^m=a^m b^m)\)

\(\sqrt[3]{8x^3 y^{12}}=(2^3)^{\frac 13} (x^3)^{\frac 13} (y^{12})^{\frac 13}\)

\(\sqrt[3]{8x^3y^{12}}=(2^{3 \times \frac 13})(x^{3 \times \frac 13}) (y^{12 \times \frac 13}) \ \ \  (\text{Since } (a^m)^n=a^{mn})\)

\(\sqrt[3]{8x^3y^{12}}=(2^1)(x^1)(y^4)\)

\(\sqrt[3]{8x^3y^{12}}=2 x y^4\)

Therefore, the given radical expression to its rational exponent form is given by \(\sqrt[3]{8x^3y^{12}}=(8x^3 y^{12})^{\frac 13}\) and the simplified form is given by \(\sqrt[3]{8x^3y^{12}}=2xy^4\)

0

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more
...