Exponent Rules
Related Pages
Exponents
Rules Of Exponents
Logarithmic Functions
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In these lessons, we will learn five rules of exponent and how to use them. These exponent rules are typically covered in Grade 7 Math.
Exponent rules (also called laws of exponents) are a set of rules that simplify expressions involving exponents.
The following table give the Exponent Rules. Scroll down the page for examples and solutions.
The rules of exponent are:
Product Rule:
xm × xn = xm+n
When we multiply two powers that have the same base, we add the exponents.
Example: 32 x 35 = 37
Power Rule:
(xm)n = xm × n
When we raise a power to a power, we multiply the exponents.
Example: (32)5 = 310
Quotient Rule:
xm / xn = xm-n (where x ≠ 0)
When we divide two powers with the same base, we subtract the exponents.
Example: 36 ÷ 32 = 34
Zero Rule:
x0 = 1 (where x ≠ 0)
Any nonzero number raised to the power of zero equals 1.
Example: 540 = 1
Negative Rule:
x-n = 1 / xn (where x ≠ 0)
Any nonzero number raised to a negative power equals its reciprocal raised to the opposite positive power.
Example: 2-3 = 1/(23)
Fractional Exponent Rule (Roots):
xm/n = n√xm = (n√x)m
A fractional exponent represents a root. The denominator of the fraction is the index of the root, and the numerator is the power.
Example: x1/2 = √x (square root)
x2/3 = 3√x2 = (3√x)2
Key Points to Remember:
- The base must be the same to use the product and quotient rules.
- A negative exponent does not make the number negative. It creates a reciprocal.
- Fractional exponents represent roots.
Introduction To Exponent Rules
Exponent Rules Song
Learn exponent rules through music!
Basic Exponent Properties
This video will illustrate the rules with a few examples.
Simple Rules Of When To Add Or Multiply The Exponents In Common Bases
Rules Of Exponents Set To Music
How To Apply The Rules Of Exponents?
Example:
Simplify the following expressions:
a) (2x34)(3xy5)2
b) (x5y9)(-5x2y2)4
Example:
Simplify the following expressions:
a) (x2/2)4
b) (4n6)2
Example:
Simplify the following expressions:
a) (3x2y4)5/(3x3y7)3
b) (5xy2)4/(5x2y)6
How To Evaluate Expressions With Negative Exponents?
Example:
Simplify the following expressions:
a) (8a6b-4)/(24a-8b9)
b) (10a2b6)(50a-3b-4)
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