How to Write Expressions as Radicals

A square root can be written as an exponent expression using mathematical shorthand.
••• Jupiterimages, Brand X Pictures/Brand X Pictures/Getty Images

Radicals, or roots, are the mathematical opposites of exponents. The smallest root, the square root, is the opposite of squaring a number, so x^2 (or x squared) = √x. The next highest root, the cube root, is equal to raising a number to the third power: x^3 = ³√x. The small 3 above the radical is called an index number, and that number represents the exponent opposite. Because of their relationship, radicals and exponents can be used to cancel each other out or to convert between each other. For example, ³√x equals x^(1/3).

    Write the expression (x^2)^(4/3) into radical form. Note that the (x^2) is the base and the (4/3) is its exponent.

    Use the base law of exponents, which states that (x^m)^n equals x^(m * n). Multiply the exponent on the base by the other exponent: x^(2 * 4/3) or x^(8/3). Note that the base law also works in the opposite direction and that x^(8/3) equals x^(8 * (1/3)). Pull the 8 out of the exponent to simplify: x^8^(1/3). Note that (1/3) is equivalent to ³√x.

    Use the cube root to cancel out the exponent: ³√(x^8). Leave the answer as it is for the radical form.

Related Articles

What Are Radicals in Math?
How to Factorise a Quadratic Expression
Negative Exponents: Rules for Multiplying & Dividing
How to Put Base Log on Graphing Calculator
How to Factor Polynomials With 4 Terms
How to Factor Monomials
How to Cross Multiply
Quotient Rule for Exponents
How to Cancel a Natural Log
What is the Identity Property of Multiplication?
How to Get Rid of Logarithms
How to Use a Calculator for Trigonometry
How to Get Rid of Cubed Power
How to Simplify Exponents
How to Evaluate Logarithms With Square Root Bases
How to Convert Pounds Per Square Foot to PSI
How to Find the X Intercept of a Function
How to Find the Slope of Linear Equations
How to Write "Three Tenths" in Standard Form
What Are Powers of Ten?