http://www.ck12.org Chapter 3. Logs and Exponents
Vocabulary
Exponentsare repeated multiplication.
Powerrefers to the number in the exponent
Power to a Poweris a number raised to an exponent which in turn is raised to another exponent.
Guided Practice
- Simplify the following expression using positive exponents.
( 26 · 83 )−^3
42 (^12 )^46413
- Simplify the following expression using only positive exponents.
((a^3 b^2 c)−^1 a^2 b^7 c)^2 - Solve the following equation using properties of exponents.
( 320.^6 )^2 =x^3
Answers: - Rewrite every exponent as a power of 2.
For example 8^3 = ( 23 )^3 = 29 and 64^13 = ( 26 )^13 = 22
( 26 · 83 )−^3
42 (^12 )^46413
=(^2
(^6) · 29 )− 3
242 −^422 =
( 215 )−^3
22 =
2 −^45
22 =
1
247
2.((a^3 b^2 c)−^1 a^2 b^7 c)^2 = (a−^3 b−^2 c−^1 a^2 b^7 c)^2 = (a−^1 b^5 )^2 =ba^102
- First work with the left hand side of the equation.
( 320.^6 )^2 =
(
( 25 )^35
) 2
= 26
26 =x^3
( 26 )^13 = (x^3 )^13
22 =x
4 =xPractice
Simplify each expression using positive exponents.
- 81−^14
- 64^23
3.( 321 )−
(^25)