G8M1 - Study Guide for Exponents and Scientific Notation

Oct 13, 2026

Upload by dawugda

Study guide covering exponent rules and scientific notation, with step-by-step methods for multiplying, dividing, and raising powers to powers using like bases. Includes guidance for converting between standard and scientific notation by moving decimals and interpreting positive versus negative exponents, plus procedures for adding and subtracting numbers in scientific form. Provides review practice: simplify exponent expressions, convert to proper scientific notation, order values by size, and apply the skills to real-world calculations using GDP comparisons and ocean-volume estimates from tank “fun facts.”

LanguageEnglish

CategoryPaper Templates

FormatPDF

Pages6

Reading Time2 min

AccessFree to download

Exponent Rules

Multiplying Exponents

Raising a Power to a Power

Dividing Exponents

Raising a Factor to a Power

Negative Exponents

Zero as an Exponent

Scientific Notation

Converting to Scientific Notation

Converting to Standard Notation

Multiplying and Dividing Scientific Notation

Adding and Subtracting Scientific Notation

Review Questions

Simplify

Convert and Order

GDP Word Problem

Ocean Volume Fish Tank Problem

NAME: Date: Mr. Rogove Math , Period Study Guide: Exponents and Scientific Notation Exponent Rules | | Description | Example | | | --- | --- | --- | --- | | Multiplying
Exponents | Add exponents with the same base | 􀀡 ! ∙ 􀀡 ! = 􀀡 !"
3! ∙ 3! = 3!
(3 is the base) | | | | Multiply any coefficient terms | 3􀀡! ∙ 5􀀡! = 15􀀡!" | | | Raising a Power to a Power | Multiply the exponents | 􀀡 ! ! = 􀀡 !" 2􀀡! ! = 2! ∙ 􀀡 !∙! = 8􀀡!" | | | Dividing Exponents | Subtract the exponents with the same base | !!􀀡
! ! = 􀀡􀀡 | | | | Divide any coefficient terms | 18􀀡3􀀡!! = 6􀀡! | | | Raising a factor to a Power | Raise the numerator and the denominator to the power | | ! 3􀀡 ! 27􀀡!
= ~~ ~~ = ~~ ~~
5! 125 | | Negative Exponents | When a number is raised to a negative exponent, change the sign of the exponent and use the reciprocal. | 1 !!
􀀡 = ~~ ~~􀀡 !
1
! !! = 􀀡􀀡 | | | Zero as an Exponent | Any number raised to the 0 power equals 1 . | 4! = 1
3􀀡 ! = 1 | | 1 G8M1: Study Guide for Exponents and Scientific Notation NAME: Date: Mr. Rogove Math , Period Scientific Notation A way to write numbers that are really big or really small. Numbers written as the product of two factors, where one factor is greater than or equal to 1 and less than 10, and the other factor is 10 raised to a power. | Converting to Scientific Notation | | | | --- | --- | --- | | Standard Notation | Scientific Notation | Explanation | | 45,000,000 (big number) | 4.5 ×10! | Move the decimal 7 places to the LEFT to make the coefficient between 1 and 10. Raise 10 to a positive power. | | 0.00000325 (small number) | 3. 25×10!! | Move the decimal 6 places to the RIGHT to make the coefficient between 1 and 10. Raise 10 to a negative power. | | Converting to Standard Notation | | | | Scientific Notation | Standard Notation | Explanation | | 1. 55×10!(big number) | 1,550,000 | Move the decimal 6 places to the RIGHT. A positive exponent means your number is greater than 10 . | | 2×10!!
(small number) | 0.00002 | Move the decimal 5 places to the LEFT. A negative exponent means your number is between 0 and 1 . | Multiplying and Dividing Scientific Notation 􀀡􀀡Multiplying: Multiply the coefficients, add the exponents, and simplify to proper scientific notation. Example: 4×10! 7×10! = 28×10! = 2. 8×10! 􀀡􀀡Dividing: Divide the coefficients, subtract the exponents, and simplify to proper scientific notation. Example: !!~~ ~~!!""!! = !! ∙ !!""!! = !! ×10! = 0. 5×10! = 5×10! Adding and Subtracting Scientific Notation Make sure your numbers are the same order of magnitude (raised to the same power often) Example: 3 × 10! + 5 × 10! = 3 × 10! + 5 × 􀀡􀀢 􀀡 × 􀀡􀀢 􀀡 = 3×10! + 500×10! = 503 × 10! = 5.03 × 10! 2 G8M1: Study Guide for Exponents and Scientific Notation NAME: Date: Mr. Rogove Math , Period Review Questions: Due when you take the test! Simplify | 7! ∙ 7! | 5! ∙ 5!! | | --- | --- | | 2􀀡 ! ∙ 5􀀡! | −6􀀡 ! ∙ 7􀀡 !! | |
!! !􀀡
|
! ! !
􀀡 􀀡
| | 5􀀡! ! | 3􀀡! !! | | 3􀀡!"􀀡 !"\# ! | 3􀀡!􀀡 ! ! | Convert the following terms to proper scientific notation, and then place order them | | Scientific Notation | Order
(1=least, 7=greatest) | | --- | --- | --- | | 0. 3×10! | | | | 401, 054×10!! | | | | 5! | | | | 3, 546, 000 | | | | 0. 0045×10!! | | | | 435×10!! | | | | 2400×10! | | | from least to greatest: 3 G8M1: Study Guide for Exponents and Scientific Notation NAME: Date: Mr. Rogove Math , Period Simplify and put into proper scientific notation | 3×10!!5×10! | 2. 5×10!!4×10!!" | | --- | --- | | 5. 2×10!
1.3 ×10! | 3. 6×10!
7. 2×10! | | 3.8 ×10! + 2.1 × 10! + 4.7 × 10! | 4.65 × 10! + 5.56 ×10! | 4 G8M1: Study Guide for Exponents and Scientific Notation NAME: Date: Mr. Rogove Math , Period Below are the gross domestic product (GDP) for select countries in the Western Hemisphere. Answer all questions below based on this table

FAQs

What are the exponent rules for multiplying and dividing powers with the same base?

When multiplying exponents with the same base, add the exponents. When dividing with the same base, subtract the exponents, then simplify.

How do you convert a big or small number between standard notation and scientific notation?

Move the decimal until the coefficient is between 1 and 10. For a big number, move left and use a positive exponent; for a small number, move right and use a negative exponent.

How are exponents and scientific notation used in the GDP and ocean volume problems?

The guide uses scientific notation to compare GDP values by size and estimate ratios, and it uses the tank “fun fact” in scientific notation to compute total ocean volume in cubic kilometers and to determine how many tanks fit the Pacific Ocean.

Oct 13, 2026

Upload by dawugda