exponent rules

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Exponent Rules : 

Exponent Rules Matina, Brooke, Anne

Multiplying : 

Multiplying If multiplying with same base Add exponents Condense expression Example: (x2) * (x6) = x8

Multiplying cont : 

Multiplying cont If exponent outside parenthesis Multiply exponents Example: (x3)4 = x12

Distribution : 

Distribution If there are two or more bases in the parenthesis with an exponent outside Distribute the exponent to both bases Example: (xy2)3 = x3y6

Distribution cont : 

Distribution cont If two bases in a fraction with an exponent outside the parenthesis Distribute exponent to both top and bottom Example:

Canceling out : 

Canceling out In a fraction with same base exponents on top and bottom You can cancel out (Dividing is like subtracting the exponents) Example: x2 /x = x

Negative exponents : 

Negative exponents If a base has a negative exponent Move the expression to the opposite side of the fraction Examples: OR

Power of 0 : 

Power of 0 Any exponent to the power of zero is 1 Examples : 40 = 1 50 = 1 89345879230=1

Common Mistakes : 

Common Mistakes Not distributing an exponent outside the parenthesis to both the variable AND coefficient Eg. (2x)5 = 32x 5 Thinking that an exponent outside the parenthesis is ADDED not MULTIPLIED Eg. (2x2) 5 = 32x10

Summary problem 1 : 

Summary problem 1 Write without negative exponents 5(x-3)-1 + 4(x+3) -2 =

Summary Problem 2 : 

Summary Problem 2 Simplify ((x2)6) -1 (x12)-1 1 x 12

Summary Problem 3 : 

Summary Problem 3 Simplify

Summary problem 4 : 

Summary problem 4 Solve for x (3x)3 =81 27x 3 = 81 x 3 = 3 x=31/3

Summary Problem 5 : 

Summary Problem 5 Solve for x 8(x-2) = 2 8/x2 = 2 8 = 2x2 4= x2 X=2 or -2