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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