Pre – Algebra
8th Grade Math
Exponent Properties and Scientific Notation Study Guide
Section EPSN – 1: Exponent Properties
• Product of Powers Property
o To multiply powers with the same base add the exponents
o [pic]
• Power of Powers Property
o To find a power of a power, multiply the exponents
o [pic]
• Power of a Product Property
o To find the power of a product, find the power of each factor and multiply
o [pic]
• Quotient of Powers Property
o To divide powers with the same base, subtract the exponents of the denominator from the exponents of the numerator
o [pic]
• Power of Quotient Property
o To find a power of a quotient, find the power of the numerator and the power of the denominator and divide
o [pic]
• Negative Exponents
o A to the negative n power is 1/a to the nth power
o [pic]
• Zero Exponents
o Anything to the power of zero is one
o [pic]
• Combining Properties
o [pic]
o [pic]
Section EPSN – 2 : Cube Roots
• Finding Cube Roots
o [pic]
o [pic]
• Word Problems
o A wooden block is a cube. It has a volume of 125 cubic centimeters. What is the length of one side of the cube?
▪ V = [pic]
▪ V = [pic]
▪ One Side has a length of 5 centimeters
o What is the area of the bottom of the cube using the information from the above problem
▪ A = L * W
▪ A = 5 * 5
▪ A = 25 centimeters squared
• Solving Cube Root Equations
o [pic]
▪ [pic]
▪ y = 5
o [pic]
▪ [pic]
▪ [pic]
▪ [pic]
▪ x=1
Section EPSN – 3: Scientific Notation
• Changing from standard form to scientific notation
o Rules
▪ A positive exponent means the number is greater than zero
▪ A negative exponent means the number is between zero and one
▪ Place the decimal point between the nonzero numbers so that the non zero number is less than ten
▪ Negative number in problem = Negative number in answer
o 120,000,000
▪ [pic]
o 0.00012
▪ [pic]
• Changing from scientific notation to standard form
o Rules
▪ Positive exponents is a number greater then zero ( move decimal point right)
▪ Negative exponent is a number less then zero ( move decimal point left)
▪ Negative number in problem = Negative number in answer
o 3.2 * 10[pic]
▪ 32,000,000
o 8.96 * 10[pic]
▪ .0000896
Section EPSN – 4: Applying Scientific Notation
• Multiplication with Scientific Notation
o [pic]
▪ [pic]
▪ [pic]
o [pic]
▪ [pic]
▪ [pic]
▪ [pic]
• Division with Scientific Notation
o [pic]
▪ [pic]
▪ [pic]
▪ [pic]
o [pic]
▪ [pic]
▪ [pic]
▪ [pic]
• Word Problems
o A rectangular section of wilderness will be set aside as a new wildlife refuge. Its dimensions are [pic]meters by [pic]meters. Find the area of the land in square meters?
▪ A = L x W
▪ A = [pic]([pic])
▪ A = [pic]
▪ A = [pic]
▪ A = [pic]square meters
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