Multiplying and Dividing Powers Section 8.2

Multiplying Powers When 2 powers have the same bases, the powers can be multiplied. a³•a² To do this, keep the base the same and add the exponent. a²⁺³ or a⁵ 3³•3² 3²⁺³ or 3⁵

Simplify Each Expression 4³•4⁵ 4³⁺⁵ or 4⁸ x³•x⁴ x³⁺⁴ or x⁷ 4y³•y⁴ 4y³⁺⁴ or 4y⁷ (4y²)(3y) (4•3)(y²⁺¹) 12y³

Your Turn! 10⁴•10² 10⁴⁺² 10⁶ y²•y⁴ y²⁺⁴ y ⁶ (-3x²)(5x) (-3•5)(x ²⁺¹) (-15)(x³ ) -15x³ (x⁵y²)(x²y⁴) (x⁵⁺²)(y⁴⁺²) x⁷y⁶

Dividing Exponents You can divide posers with the same base by subtracting the exponents a⁵ a² = a⁵⁻² =a³ Think about it: a a a a a a a

Dividing Exponents 5⁷ 5⁴ =5⁷⁻⁴ =5³ x⁶y⁴ xy² =x⁶⁻¹y⁴⁻² =x⁵y²

Simplify Each Expression 4x⁷ 4x⁴ (4 4) and (x⁷⁻⁴) =x³ 8m⁴n⁵ 2m³n² (8 2) and (m⁴⁻³) and (n⁵⁻²) = 4m¹n³ Now, SIMPLIFY! 4mn³

Your Turn! 10⁵ 10² = 10⁵⁻² = 10³ y⁵ y⁴ = y⁵⁻⁴ = y ¹ = y a⁴b⁸ ab² = a⁴⁻¹ and b⁸⁻² = ab⁶ -30m⁵n² 10m³n (-30 10) & m⁵⁻³ & n²⁻¹ = -3m²n

Remember… Any base with an exponent of zero will always equal 1! 100⁰ = 1 (-12ab)⁰ = 1

More Practice a³b⁴ a³b (a³⁻³ )(b⁴⁻ ¹) a⁰b³ SIMPLIFY = b³ (Remember a⁰ = 1)  10x⁴y³ 5x⁴y² (2)(x⁴⁻⁴)(y³⁻²) 2x⁰y ¹ SIMPLIFY = 2y

Review Simplify Each Expression n⁸ n⁵ =n³ ab⁵c ac =b⁵ ¾a(12b²) =9ab² y²•y⁵ =y⁷ (t²)(t²)(t) =t⁵ (3a²)(4a³) =12a⁵ n⁸ n⁵ =n³ ab⁵c ac =b⁵ ¾a(12b²) =9ab²

Homework  Pg. 344 3-14all, 16-44even