The exponent rules become machinery this week. Same base multiplied: add the exponents. A power raised to a power: multiply them. A product raised to a power: everyone inside gets the exponent.
What you have to be able to do
Multiply powers with the same base
Raise a power to a power
Raise a product to a power
The procedures
Product of powers
Same base multiplied: keep the base, add the exponents.
x3 · x4 stacks three x’s with four more.
Different bases do not combine this way.
Power of a power
A power raised to a power: multiply the exponents.
(x3)4 is four copies of three copies.
The base stays as it is.
Power of a product
Every factor inside the parentheses receives the exponent.
(2x)3 is 23 times x3.
Numbers get computed; letters keep their exponents.
Worked
WORKED
Simplify x3 · x4. Same base: add the exponents. 3 + 4 is 7. ANSWER: x7
WORKED
Simplify (2x2)3. The 2 and the x2 each take the cube. 23 is 8, and (x2)3 is x6. ANSWER: 8x6
Terms
Term
Meaning
monomial
a single term: a number, a letter, or their product
product of powers
same base multiplied: add the exponents
power of a power
a power raised to a power: multiply the exponents
Check yourself
1. Simplify: x5 · x2
2. Simplify: (x3)4
3. Simplify: (3x)2
reveal answers
x7 · x12 · 9x2
This page is the summary, not the lesson. The full working, every step of every example, is on the board in class. Come here to remember what the week was about. Go there to learn how it is done.
-- THE UNKNOWN -- week 11, exponents and powers of productsalgebra 1 · oda