Power Play — Formula Sheet

n × n × ... (a times) = n^a

5^4 = 5 × 5 × 5 × 5 = 625

x^0 = 1

2^(-1) = 1/2

n^a ÷ n^b = n^(a-b)

32400 = 2^4 × 5^2 × 3^4

10 × 10 × ... (n times) = 10^n

5-digit password combinations = 10^5

3-digit lock combinations = 1000

2-digit lock combinations = 100

2^4 ÷ 2^3 = 2^(4-3) = 2^1

2^0 = 1

2^4 ÷ 2^5 = 2^(-1) = 1/2

2^4 ÷ 2^10 = 2^(-6) = 1/64

4^7 ÷ 4^5 = 4^2

5^4 = 5 × 5 × 5 × 5 = 625.

Estu has 4 dresses and 3 caps, so the number of combinations is 4 × 3 = 12.

2^4 ÷ 2^3 = 2^(4-3) = 2^1 = 2.

For a non-zero base, x^0 = 1.

5^4 = 625.

4 + 4 + 4 = 3 × 4 = 12, but 4 × 4 × 4 = 4^3 = 64.

A 2-digit lock has 100 combinations, a 3-digit lock has 1000 combinations, and a 5-digit lock has 10^5 = 1,00,000 combinations.