Algebra 2 Practice - Write a Radical Expression in Exponential Form (Example 1)

Please subscribe!    / nickperich   *Algebra 2 Practice - Write a Radical Expression in Exponential Form* A *radical expression* can be rewritten as an *exponential expression* using the property of exponents. The general rule is: \[ \sqrt[n]{a} = a^{\frac{1}{n}} \] In this case: The *radical* \( \sqrt[n]{a} \) represents the *n-th root* of \( a \). The *exponent* \( \frac{1}{n} \) represents taking the *n-th root* of \( a \). **Steps to Rewrite a Radical Expression in Exponential Form**: 1. *Identify the index* of the radical (the number under the root). This becomes the denominator of the fraction exponent. 2. **Identify the expression inside the radical**. This becomes the base of the exponential expression. 3. *Write the exponent as \( \frac{1}{n} \)* where \(n\) is the index of the root. --- *Example 1:* Rewrite \( \sqrt{a} \) in exponential form. 1. The radical has no index, so the index is 2, which represents a **square root**. 2. The expression inside the radical is \( a \). Therefore, \( \sqrt{a} \) becomes: \[ \sqrt{a} = a^{\frac{1}{2}} \] --- *Example 2:* Rewrite \( \sqrt[3]{b} \) in exponential form. 1. The index of the radical is 3, which represents a **cube root**. 2. The expression inside the radical is \( b \). Therefore, \( \sqrt[3]{b} \) becomes: \[ \sqrt[3]{b} = b^{\frac{1}{3}} \] --- *Example 3:* Rewrite \( \sqrt[4]{x^2} \) in exponential form. 1. The index of the radical is 4, which represents a **fourth root**. 2. The expression inside the radical is \( x^2 \). Therefore, \( \sqrt[4]{x^2} \) becomes: \[ \sqrt[4]{x^2} = x^{\frac{2}{4}} = x^{\frac{1}{2}} \] --- *Example 4:* Rewrite \( \sqrt[5]{y^3} \) in exponential form. 1. The index of the radical is 5, which represents a **fifth root**. 2. The expression inside the radical is \( y^3 \). Therefore, \( \sqrt[5]{y^3} \) becomes: \[ \sqrt[5]{y^3} = y^{\frac{3}{5}} \] --- *Example 5:* Rewrite \( \sqrt[7]{z^4} \) in exponential form. 1. The index of the radical is 7, which represents a **seventh root**. 2. The expression inside the radical is \( z^4 \). Therefore, \( \sqrt[7]{z^4} \) becomes: \[ \sqrt[7]{z^4} = z^{\frac{4}{7}} \] --- **Summary**: To rewrite a radical expression in **exponential form**, use the formula: \[ \sqrt[n]{a} = a^{\frac{1}{n}} \] The *index* of the radical becomes the *denominator* of the fractional exponent. The *expression inside the radical* is the *base* of the exponential expression. I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out: / nickperich Nick Perich Norristown Area High School Norristown Area School District Norristown, Pa #math #algebra #algebra2 #maths #math #shorts #funny #help #onlineclasses #onlinelearning #online #study