How to Solve Rational Exponents and Radicals?
By identifying powers and roots and converting them to radicals, we can write rational power exponents expressions as radicals. In this post, you learn more about rational exponents and radicals.
An expression with a rational exponent is equivalent to a radical in which the denominator is the index and the numerator is the exponent. Any radical expression can be written with a rational exponent, which we call exponential form.
Related Topics
A step-by-step guide to rational exponents and radicals
By identifying powers and roots and converting them to radicals, we can write rational power exponents expressions as radicals. Consider the rational exponents’ expression \(a^{\frac{m}{n}}\). Now, follow the steps given:
- Identify power by looking at the numerator of the rational exponent. Here in the rational exponent \(a^{\frac{m}{n}}\), \(m\) is the power.
- Identify the root by looking at the denominator of the rational exponent. Here in rational exponent \(a^{\frac{m}{n}}\), \(n\) is the root.
- Write the base as the radicand, power raising to the radicand, and the root as the index. Here we can write \(a^{\frac{m}{n}}=\sqrt[n]{a^m}\).
We can also convert radicals into rational exponents. Consider the square root of the positive number \(\sqrt{a}\). We can write the square of \(\sqrt{a}\) as a rational exponent. \(\sqrt{a}=a^{\frac{1}{2}}\) which is a rational exponent.
Rational Exponents and Radicals – Example 1:
Express \((2x)^{\frac{1}{3}}\) in radical form.
Solution:
\((2x)^{\frac{1}{3}}\) \(=\)\(\sqrt[3]{2x}\)
Rational Exponents and Radicals – Example 2:
Write \(\sqrt[4]{81}\) as an expression with a rational exponent.
Solution:
\(\sqrt[4]{81}=81^{\frac{1}{4}}\)
Exercises for Rational Exponents and Radicals
Rewrite the expression in radical form or rational exponent.
- \(\color{blue}{6\sqrt[3]{xy}}\)
- \(\color{blue}{27^{\frac{2}{3}}}\)
- \(\color{blue}{\sqrt[2]{\left(5ab\right)^3}}\)
- \(\color{blue}{\left(10\:r\right)^{-\frac{3}{4}}}\)
- \(\color{blue}{\frac{1}{\sqrt[5]{\left(6x\right)^3}}}\)
- \(\color{blue}{6\left(xy\right)^{\frac{1}{3}}}\)
- \(\color{blue}{\sqrt[3]{27^2}}\)
- \(\color{blue}{\left(5ab\right)^{\frac{3}{2}}}\)
- \(\color{blue}{\frac{1}{\sqrt[4]{\left(10\:r\right)^3}}}\)
- \(\color{blue}{\left(6x\right)^{-\frac{3}{5}}}\)
Related to This Article
More math articles
- Linear, Quadratic, and Exponential Models
- How to Solve Systems of Linear Inequalities?
- The Application of The Squeeze Theorem: Limit Problems Made Easy
- What Is a Good ALEKS Score?
- How to Write a Quadratic Function from Its Vertex and Another Point
- The Ultimate 7th Grade TCAP Math Course (+FREE Worksheets)
- How to Graph a Horizontal or Vertical line?
- How to Identify Statistical Questions
- Driving Electric Is Cheaper: Let’s Do the Math
- 7th Grade MCAP Math Worksheets: FREE & Printable
What people say about "How to Solve Rational Exponents and Radicals? - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.