Download 6th Exponents Notes

Exponents Notes
When we want to show repeated addition, we use the times symbol ×
5 times 3 is really just “5 groups of 3” or “5 3’s added together”. What if we want to show
repeated multiplication? This is where exponents come in handy.
An exponent is a number that indicates how many times a number is multiplied by itself.
An exponents or powers are analogous to multiplication.
Ex: How is exponentiation similar to multiplication?
Ex: write 4 × 4 × 4 × 4 using an exponent.
Ex: write 63 as a product of the same factor. Then find what that value is.
Practice: write each product using an exponent.
1. 2 × 2 × 2 × 2
4. 7 × 7 × 7
2. 10 × 10 × 10
5. 2.4 × 2.4
3.
1
4
1
1
1
1
×4×4×4×4
6. 6 × 6 × 6 × 6 × 6 × 6
Practice: write each power as a product of factors. Then find the value.
1.
73
2.
27
3.
3.12
4.
1
(3)3
Exponents also have special rules to follow
Exponent Rules:
Ex:
Ex:
23 × 22 =
43 × 42 =
32 × 34 =
𝑥3 × 𝑥7 =
37 ÷ 34 =
(−6)6 ÷ (−6)3 =
44 ÷ 4 =
𝑤 11 ÷ 𝑤 4 =
Ex:
(23 )2 =
(42 )5 =
((−1)6 )3 =
(𝑎10 )4 =
Ex:
[2 × (−3)]4 =
Ex:
(3)3 =
Ex:
20220 =
2−3 × 23 =
2−2 =
(−5)−3 =
2