Laws of Indices
What is the rule for multiplying positive indices?
When multiplying, add the exponents.
Simplify 4⁵ x 3⁴ x 4²
4⁷ x 3⁴
Solve 2³ x 2⁰
8
Solve 6³ x 6-³
1
2^x =512
What is x? (no calculator)
x=8
What is the rule for dividing positive indices?
When dividing, subtract the exponents
Simplify 2⁴ x 5⁷ x 5³ x 6² x 6⁸
2⁴ x 5¹⁰ x 6¹⁰
Solve 4² x 8⁰
16
Solve 4 x 2-³
1/2
3^x=243
x=5
What is the rule for the zero index?
Anything raised to a 0 is a 1
Simplify 3⁹÷3²
3⁷
Solve (4⁰)²
1
Solve 5÷2-²
20
(⅓)^x =81
Find x
x = -4
What are the rules for negative indices?
Change the negative index to the positive side by using the reciprocal.
Simplify
(6³ x 6³ x 8⁵ x 8⁶) / (8⁶ x 6²)
6⁴ x 8⁵
What is 2-3 as a decimal? (without a calculator!)
0.125
Solve 8-⁶÷8-⁴
(Give answer using a positive index)
1/8²
4^-x=⅟₁₆
Find x
x=2
Solve 3x⁷y⁵z³÷9x⁴y³z
x³y2z²÷3
Solve 4³ x 3⁷ x 4-³ x 3-⁵
9
Solve 100 x 10-¹
10
6^z=36^z
z=0