Algebra 1 > Notes > Yorkcounty Final > Unit 5 > Lesson 10 - Exponents

Exponents Lesson 10

Properties of Exponents • x4 • x is called your base • 4 is your exponent • This is read x to the 4th power. • NOTE: x does have an exponent and it is 1. So x is the same as x1.

Properties • x3 + x4 , can we add these things? • NO! They are not like terms. So what can we do with them? • We can multiply them! • Like terms have same bases and same exponents. We do have like bases here but we do not have like exponents. No adding between these two things.

Properties • (x3) . (x4) • First we want to know what x3 and x4 means? • x . x . x = x3 • x . x . x . x = x4 • (x3)(x4) = (x.x.x)(x.x.x.x) = (x.x.x.x.x.x.x) = x7

Properties • Lets try x3. x2 • (x.x.x).(x.x) = x5 • We can now talk about a rule. When you multiply like bases add the exponents. • xa . xb = x(a + b)

Try this one • • • • •

x23 . x45 = ? Do we have like bases? YES! Are we multiplying? YES! So we add exponents x23 . x45 = x(23 + 45) = x68

Try these • • • •

x4 . x 9 = ? x . x5 = ? 2x6 . 4x6 = ? x . x. x = ?

Answers on the next slide.

Answers • • • •

1) x13 2) x6 3) 8x12 4) x3

More Properties x x⋅ x⋅ x⋅ x⋅ x 3 = = x ⋅ x ⋅ x = x 2 x x⋅ x 5

When we expand the exponents we get 5 x’s on the top and 2 on the bottom. We can take away two from the top and two from the bottom. We are left with 3 x’s on the top.

Division Property a

x a −b = x b x

Example 5

x 5− 2 3 = x = x 2 x

Try this one Reduce:

6

x 4 x

Answer • x(6-4) = x2

Power of a Power Property • (xm)n = xmn • When you have an exponent raised to another exponent you MULTIPLY the exponents. • So (x2)5 = x10

Try these • (x6)5 • (x4)12 • x4 . x 7

Answers • (x6)5 = x11 • (x4)12 = x48 • x4 . x7 = x4 +7 = x11 (multiply same bases add exponents)

Power of a Product Rule • (ab)x = ax . bx • When you have an exponent outside the parentheses it gets distributed to everything on the inside. • (xy)5 = x5 . y5

Try this • (xb)11

• Answer is… • x11 . b11