7.5 DIVISION AND EXPONENTS: Base: A number that is multiplied repeatedly. Exponent: A number that shows repeated multiplication. Property: A character or attribute that something has.

GOAL:

Remember: An exponent equation has two components: Base Exponent

PROPERTIES: Dividing with Exponents For every number a≠0 and m, n, are integers, Ex: = = 3 2 = 9

YOU TRY IT:

SOLUTION: Always move the smaller exponent to the opposite side.

PROPERTIES: Dividing with Exponents For every number a≠0, b ≠0 and m an integers, Ex:

YOU TRY IT: Simplify:

SOLUTION: With parenthesis, the exponent distributes to the numerator and denominator:

PROPERTIES: Dividing with Exponents For every number a≠0 and m, n, are integers, Ex: = 1.5x 10 2 =8.8x 10 -8

YOU TRY IT:

SOLUTION: With scientific notation, we divide the numbers and subtract/add the exponents of the base 10.

VIDEO: Dividing With Exponents Dividing Powers equations/exponent-properties-algebra/v/exponent- properties-4

REMEMBER THE PROPERTIES:

PROPERTIES: ZERO: as an exponent For every number a, Ex: 4 0 = 1 (-3) 0 = = 1 1,000,000 0 = 1 -½ 0 = -1

PROPERTIES: Negative numbers: as an exponents For every nonzero number a≠0, and integer n Ex:

PROPERTIES: Multiplying powers with same base: For every number a≠0 and m, n, are integers, Ex: 1) 4 1 ∙ 4 3 = = 4 4 = 256

PROPERTIES: Raising powers to powers: For every number a≠0 and m, n, are integers, Ex: 1) (4 1 ) 3 2) (3 1 ) -3 = 4 1∙3 = 4 3 = 64 = 3 1 ∙ -3 = 3 -3

PROPERTIES: Raising a product to powers: For every number a≠0 and m, n, are integers, Ex: 1) (4x) 3 2) (3s) -3 = 4 3 x 3 = 64x 3 = 3 -3 s -3

PROPERTIES: Dividing with Exponents For every number a≠0 and m, n, are integers, Ex: = = 3 2 = 9

PROPERTIES: Dividing with Exponents For every number a≠0, b ≠0 and m an integers, Ex:

PROPERTIES: Multiplying and Scientific notation For every nonzero number a, b and integer n and m (a×10 n )(b×10 m ) = a∙b×10 n+m

PROPERTIES: Multiplying and Scientific notation For every nonzero number a, b and integer n and m (a×10 n ) c (b×10 m ) = a c ∙b×10 (n)(c)+m

PROPERTIES: Dividing with Exponents For every number a≠0 and m, n, are integers, Ex: = 1.5x 10 2 =8.8x 10 -8

VIDEOS: Exponents and Division xponents-radicals/exponent- properties/v/exponent-properties-involving- quotients

CLASSWORK: Page : Problems: As many as needed to master the concept