# Exponents and Roots

An exponent is a superscript number placed next to another number at the top right. It indicates how many times the base number is to be multiplied by itself. Exponents provide a shorthand way to write what would be a longer mathematical expression. Example: a^{2}=a×a; 2^{4}=2×2×2×2. A number with an exponent of 2 is said to be “squared,” while a number with an exponent of 3 is said to be “cubed.” The value of a number raised to an exponent is called its power. So, 8^{4} is read as “8 to the 4th power,” or “8 raised to the power of 4.” A negative exponent is the same as the reciprocal of a positive exponent. Example: a^{(-2)}=1/a^{2}. A root, such as a square root, is another way of writing a fractional exponent. Instead of using a superscript, roots use the radical symbol (√) to indicate the operation. A radical will have a number underneath the bar, and may sometimes have a number in the upper left: √(n&a), read as “the nth root of a.” The relationship between radical notation and exponent notation can be described by this equation: √(n&a)=a^{(1/n)}. The two special cases of n=2 and n=3 are called square roots and cube roots. If there is no number to the upper left, it is understood to be a square root (n=2). Nearly all of the roots you encounter will be square roots. A square root is the same as a number raised to the one-half power. When we say that a is the square root of b (a=√b), we mean that a multiplied by itself equals b: (a×a=b).

## Free Exponents and Roots Fact Sheet

Use the exponents and roots fact sheet below to help you get a better understanding of how exponents and roots work. You are encouraged to print or download the exponents and roots fact sheet with the PDF link at the bottom of the page.

Download Exponents and Roots PDF

Provided by:

*Mometrix Test Preparation*

Last updated: 01/25/2018

Find us on Twitter: Follow @Mometrix