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 Get Rid of Logarithms
How to Solve Large Exponents
How to Factorise a Quadratic Expression
How to Calculate Exponents
Quotient Rule for Exponents
How to Do Powers in Math
How to Put Base Log on Graphing Calculator
How to Cross Multiply
How to Convert Quadratic Equations From Standard to...
How to Factor Monomials
How to Cancel a Natural Log
How to Evaluate Logarithms With Square Root Bases
How to Solve Distributive Properties With Fractions
How to Subtract Monomials & Binomials
How to Factor Binomial Cubes
What Is the Square Root Method?
How to Find the Slope of Linear Equations
How to Calculate the Volume of a Triangle
What is the Identity Property of Multiplication?