How to Manipulate Roots & Exponents

••• NA/ Images

Manipulating roots and exponents is one of the basic components of algebra. You will have to learn how to perform operations with roots and exponents in high school and college algebra classes, as well as in career fields that rely heavily on math, such as engineering. In order to manipulate roots and exponents, refer to a set of algebraic rules.

    Realize that a number or variable to the first power remains the same. For example, a^1 = a.

    Add exponents that have the same base in a multiplication problem. For instance, y^3 x y^4 = y^3+4. Therefore the answer is y^7.

    Multiply multiple exponents belonging to one base. For example, x^(2)(3) = x^2x3, which equals x^6.

    Subtract exponents of like bases in division problems. For instance, a^5 / a^2 = a^5-2, which equals a^3.

    Realize that any number or variable raised to the zero power equals 1.

    Treat negative exponents in a reciprocal fashion. For instance, x^-3 = 1/x^3.

    Divide exponents when a root sign is involved. For instance if there is a 2 exponent on the left side of the square root sign and an x^3 under the square root sign, the answer would be x^3/2.

    Realize that the square root of two multiplied variables equals the product of each variable squared. For example, the square root of xy equals the square root of x times the square root of y.

    Realize that the quotient of two variables under a square root sign equals the square root of the top variable divided by the square root of the bottom variable. For instance, the square root of x/y equals the square root of x divided by the square root of y.

Related Articles

How to Simplify Monomials
How to Solve Distributive Properties With Fractions
How to Get Rid of a Variable That Is Cubed
How to Get Rid of Cubed Power
How to Do Exponents Outside of the Parenthesis
How to Divide Rational Numbers
How to Help With Polynomials
How to Integrate the Cube Root of X
What is the Identity Property of Multiplication?
How to Simplify Exponents
How to Do Fractions on a TI-30X IIS
10 Laws of Exponents
How to Classify Polynomials by Degree
How to Square a Fraction With a Variable
How to Find the Height of a Rectangular Pyramid
Laws of Exponents: Powers & Products
How to Divide Ratios
Tips for Multiplying Radicals
How to Multiply Rational Fractions With Two Variables
How to Simplify Algebraic Expressions