Advanced · 15 min
Powers and roots
Use exponent rules and distinguish square roots from equation solutions.
Combine powers with the same base
When multiplying powers with the same base, add their exponents. When dividing, subtract exponents; the base must be nonzero for division.
Worked example
2³ × 2² = 2⁵ = 32; 5⁴ ÷ 5² = 5² = 25
Interpret roots and negative exponents
A negative exponent means a reciprocal. The square-root symbol denotes the nonnegative root, whereas an equation such as x² = 9 has both 3 and −3 as solutions.
Worked example
2⁻³ = 1/8; √49 = 7; x² = 49 gives x = ±7.
Check an exponent rule
- Calculate 4³ ÷ 4² using both the exponent rule and direct division.
- Explain why √16 is 4 but x² = 16 also has the solution −4.