Powers and Laws of Exponents SWBAT write the standard form for numbers that are given in exponential form; write the exponential form for numbers that are given in standard form; apply the multiplication and division laws of exponents; identify the value of a number to the zero power; simplify expressions with exponents.

Definitions  Exponent – tells you how many times a number is used as a factor (how many times you multiply it)  Base – The factor (number) being multiplied

3 ways to write exponents Exponential Form Factored Form Standard Form x 10 x 10 1,000 1, x 6 x 6 x 6 x 6 100,000 5x5x5x5x5x5x5x5x51,953, , x10x10x10x10

Write each in simplest exponential form  6 · 6 · 6 · 7 · 7  -1(-1)(-2)(-3)(-3)  2 · 2 · 2 · 2 · 2 · 2 · 2  10 · 10 · 10 · 10 · 10 · 10 · 10 · 10

Multiplying Exponents  When they have the same base, keep the base number and add the exponents  2 · 2 2 · 2 4  5 · 5 3  14 6 · 14 8

Dividing Exponents  When dividing exponents with the same base, keep the base and subtract the exponents.  10 9 ÷ 10 5  13 8 ÷ 13 2 _56__56__56__56_