Exponents & Powers
Grades 6–8 Algebra Powers
2⁵ means 2 multiplied by itself 5 times:
2·2·2·2·2 = 32. The base is 2, the
exponent is 5. Exponents are just repeated
multiplication written small.
The three big rules
- Multiply powers → add exponents: x³ · x² = x⁵ (three x's · two x's = five x's)
- Divide powers → subtract exponents: x⁵ ÷ x² = x³
- Power of a power → multiply exponents: (x²)³ = x⁶
4³ · 4² = 4⁵ = 1024
x⁷ ÷ x³ = x⁴
(y²)⁴ = y⁸
Zero and negative exponents
x⁰ = 1— anything to the zero is 1. Why? x³ ÷ x³ = 1 and = x⁰, so they must be the same.x⁻ⁿ = 1/xⁿ— a negative exponent means "one over." 2⁻³ = 1/8.
Watch out
(2x)³ = 8x³, not 2x³ — the power hits the
whole inside. And −3² = −9 but
(−3)² = 9: without parentheses the negative isn't
squared.
Connection
Exponents are why scientific notation
works: 6.02 × 10²³ is just powers of ten doing the heavy lifting.
Practice
4⁴ = ___
Simplify x⁴ · x⁵ (write like x^9)
5⁻² equals:
99⁰ = ___
Next: square roots · Back: inequalities