01 Key Concepts
Base and Exponent
In x^n, x is the base (the number being multiplied) and n is the exponent (how many times to multiply it).
Exponent of 1 and 0
Any number to the power of 1 equals itself: x^1 = x. Any nonzero number to the power of 0 equals 1: x^0 = 1.
Product Rule
When multiplying powers with the same base, add the exponents: x^a * x^b = x^(a+b).
Quotient Rule
When dividing powers with the same base, subtract the exponents: x^a / x^b = x^(a-b).
Power of a Power Rule
When raising a power to another power, multiply the exponents: (x^a)^b = x^(a*b).
Negative Exponents
A negative exponent means take the reciprocal: x^(-n) = 1/(x^n).
02 Key Formulas
- x^a * x^b = x^(a+b)
- x^a / x^b = x^(a-b)
- (x^a)^b = x^(a*b)
- x^(-n) = 1/(x^n)
03 Solved Examples
Example 1 Evaluate 2^4.
- This means 2 multiplied by itself 4 times: 2*2*2*2.
- 2*2=4, 4*2=8, 8*2=16.
Answer: 16
Example 2 Simplify x^3 * x^5.
- Apply the product rule: add the exponents.
- 3 + 5.
Answer: x^8
Example 3 Simplify (x^2)^4.
- Apply the power of a power rule: multiply the exponents.
- 2 * 4.
Answer: x^8
04 Practice Questions
1Evaluate 3^2.
9
2Evaluate 5^0.
1
3Simplify x^4 * x^2.
x^6
4Simplify x^7 / x^3.
x^4
5Simplify (x^3)^2.
x^6
📄 Exponents — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.