Bases and Exponent Rules

Question 1

1) Any number to the zero power always equals…

Answer 1

1

Examples:

x⁰ = 1

5⁰ = 1

129⁰ = 1

Question 2

2) Any number to a negative exponent is…

Answer 2

the reciprocal of that number to its positive exponent

Examples:

x^-4 = 1/x⁴

5^-3 = 1/5³

129^-1 = 1/129

Question 3

3) When you raise 10 to a power, you get…

Answer 3

1 followed by the number of zeros equal to that power

Examples:

10² = 100 (two zeros)

10³ = 1,000 (three zeros)

10⁴ = 10,000 (four zeros)

Question 4

4) To multiply like bases, you…

Answer 4

add their exponents

Example:

x³ × x² = x^{(3 + 2)} = x⁵

Question 5

5) To divide like bases, you…

Answer 5

substract the exponents

Example:

x⁵ ÷ x² = x^{(5 - 2)} = x³

Question 6

6) Multiply the exponents of a base inside and outside of parentheses

Answer 6

Example:

(x²)³ = x^{(2 × 3)} = x⁶