Exponents with decimal and fractional bases
Key Notes :
Understanding Exponents with Decimal Bases
- Exponents can also be applied to decimal numbers.
- The rules for exponents remain the same, regardless of whether the base is an integer, decimal, or fraction.
Examples:
- (0.5)² = 0.5 * 0.5 = 0.25
- (1.2)³ = 1.2 * 1.2 * 1.2 = 1.728
Understanding Exponents with Fractional Bases
- Exponents can also be applied to fractions.
- When raising a fraction to a power, raise both the numerator and denominator to that power.
Examples:
- (2/3)² = (2²) / (3²) = 4/9
- (5/7)³ = (5³) / (7³) = 125/343
Learn with an example
Evaluate. Write your answer as a decimal or whole number.
(0.03)2 = _______
The base is 0.03 and the exponent is 2. Use 0.03 as a factor 2 times.
(0.03)2 =0.03 · 0.03=0.0009
Evaluate. Write your answer as a fraction or whole number.
(1/3)3 =_______
(1/3)3 =1/3 × 1/3 × 1/3
=1/3 × 3 × 3
=1/27
Evaluate. Write your answer as a fraction or whole number.
(1/2)3 =______
(1/2)3 =1/2 × 1/2 × 1/2
=1/2 × 2 × 2
=1/8
let’s practice!
