5. Exponents

Practice: (2a)²

(2a)² = 2²a² = 4a²

Practice: Multiplying with Exponents (2x²)(3x³)

(2x²)(3x³) = (2*3)(x²*x³) = 6(x²⁺³) = 6x⁵

Practice: Division with Exponents (3n⁶)/n²

(3n⁶)/n² 6-2 = 4 and 6 is bigger, so... (3n⁶)/n² = 3n⁶⁻² = 3n⁴

Practice: Division with Exponents (5x⁴)/(x⁶)

(5x⁴)/(x⁶) Because 6 is bigger than 4... (5x⁴)/(x⁶) = (5)/(x⁶⁻⁴) = 5/x²

Practice: (ab)³

(ab)³ = (ab)(ab)(ab) = a³b³

Practice: Division with Exponents (a⁵b⁴)/(a³b)

(a⁵b⁴)/(a³b) = (a⁵⁻³)(b⁴⁻¹) = a²b³

What if you have an expression like (xy)²?

(xy)² = (xy)(xy) = x²y²

Practice: Finding the Power of a Power of a Number (y⁸)²

(y⁸)² 8*2 = 16 so... (y⁸)² = y¹⁶

Division with Monomials Example: 2a ÷ a

Example: 2a ÷ a 2a ÷ a = (2 * a)/(a) Then, the a's will cancel out and you get... 2

Practice: Division with Monomials x⁴/x

x⁴/x = (x*x*x*x)/(x) One x from the top will cancel with the x on the bottom so you are left with... (x*x*x) = x³

Practice: Multiplying with Exponents x⁵*x⁷

x⁵*x⁷ = x⁵⁺⁷ = x¹²

Exponent Rules for Division

If the exponent on top is greater than the exponent on the bottom, you subtract the bottom number from the top number. Example: x⁵/x³ = x⁵⁻³ because 5 is more than 3. If the exponent on bottom is greater than the exponent on the top, you subtract the bigger number from the smaller number and put it on bottom. Example: x²/x⁴ = 1/x⁴⁻² = 1/x² because and 4 is more than 2.

Multiplying Monomials

Remembers that x² = x*x and x³ = x*x*x. So, you can do: x²*x³ = (x*x)(x*x*x) = x⁵

How to find the power of a power of a number Example: (x⁴)³

To find the power of a power of a number, MULTIPLY the exponents. Example: (x⁴)³ = x¹²

Multiplying with Exponents

When you multiply two powers of the same number, ADD the exponents. Example: x³ * x⁶ = x⁶⁺³ = x⁹

Practice: Multiplying with Exponents n³*n

n³*n = n ³⁺¹ = n⁴ Remember that n = n¹