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This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

- Welcome
- Learning Math Strategies (Online)Toggle Dropdown
- Study Skills for MathToggle Dropdown
- Business MathToggle Dropdown
- Place Value in Decimal Number Systems
- Arithmetic Operations
- Basic Laws
- Operations on Signed numbers
- Order of Operations
- Some Useful Basic Numeracy
- Decimals
- Fractions
- Percents
- Ratios and Proportions
- Exponents
- Statistics
- Trade and Cash Discounts
- Multiple Rates of Discount
- Payment Terms and Cash Discounts
- Markup
- Markdown
- Simple Interest
- Equivalent Values
- Compound Interest
- Equivalent Values in Compound Interest
- Nominal and Effective Interest Rates
- Annuities

- Hospitality MathToggle Dropdown
- Engineering MathToggle Dropdown
- Basic Laws
- Operations with Numbers
- Prime Factorisation and Least Common Multiple
- Fractions
- Exponents
- Reducing Radicals
- Factoring
- Rearranging Formulas
- Solving Linear Equations
- Areas and Volumes of Figures
- Congruence and Similarity
- Functions
- Domain and Range of Functions
- Basics of Graphing
- Transformations
- Graphing Linear Functions
- Graphing Quadratic Functions
- Solving Systems of Linear Equations
- Solving Quadratic Equations
- Solving Higher Degree Equations
- Trigonometry
- Graphing Trigonometric Functions
- Graphing Circles and Ellipses
- Exponential and Logarithmic Functions
- Complex Numbers
- Number Bases in Computer Arithmetic
- Linear Algebra
- Calculus
- Set Theory
- Modular Numbers and Cryptography
- Statistics
- Problem Solving Strategies

- Upgrading / Pre-HealthToggle Dropdown
- Basic Laws
- Place Value in Decimal Number Systems
- Decimals
- Significant Digits
- Prime Factorisation and Least Common Multiple
- Fractions
- Percents
- Ratios and Proportions
- Exponents
- Metric Conversions
- Reducing Radicals
- Factoring
- Solving Linear Equations
- Solving Quadratic Equations
- Polynomial Long Division
- Exponential and Logarithmic Functions
- Statistics

- Nursing MathToggle Dropdown
- Arithmetic Operations
- Place Value in Decimal Number Systems
- Decimals
- Fractions
- Percents
- Ratios and Proportions
- Interpreting Drug Orders
- Oral Dosages
- Dosage Based on Size of the Patient
- Parenteral Dosages
- Intravenous (IV) Administration
- Infusion Rates for Intravenous Piggyback (IVPB) Bag
- General Dosage Rounding Rules

- Transportation Math
- PhysicsToggle Dropdown

The exponent of a number indicates the number of times the base number is multiplied by itself. For example,

\[2^4=2\times 2\times 2\times 2 \qquad \left(\frac{1}{2}\right)^2 = \frac{1}{2} \times \frac{1}{2}\]

**Laws of exponents: **These laws help you simplify exponents.

\[b^n \cdot b^m = b^{n+m}\]

When multiplying by the same base, the exponents can be added together. For example,

\[3^4 \cdot 3^2 = \left(3\times 3\times 3\times 3\right) \cdot \left(3\times 3\right) = \left(3\times 3\times 3\times 3\times 3\times 3\right) =3^{4+2} = 3^6\]

\[b^n \div b^m = b^{n-m}\]

When dividing by the same base, the exponents can be subtracted, top minus bottom. For example,

\[\frac{5^4}{5^2} = \frac{5\times 5\times 5\times 5}{5\times 5} = 5 ^{4-2} = 5^2\]

\[\left(b^n\right)^m = b^{n\times m}\]

When multiple exponents are on a base, the exponents can be multiplied together. For example,

\[\left(7^2\right)^3 = \left(7\times 7\right)^3 = \left(7\times 7\right)\left(7\times 7\right)\left(7\times 7\right) = 7^{2\times 3} = 7^6\]

**Negative Exponents:**

A negative exponent signals a reciprocal of the base and exponents. Once the reciprocal is performed, the negative exponent becomes positive.

\[2^{-3}=\frac{1}{2^3}=\frac{1}{8}\]

This can also be interpreted as moving a value from the top of the fraction to the bottom and vice versa.

\[\frac{1}{4^{-3}}=\frac{4^3}{1}=64\qquad \frac{3^{-5}}{2^{-2}} = \frac{2^{2}}{3^{5}} = \frac{4}{243} \]

**Power of 1:**

Any base to the exponent of 1 equals itself.

\[13^1=13 \qquad \pi^1=\pi \qquad (2.2)^1=2.2\]

**Power of 0:**

Any non-zero number with the exponent 0 equals to 1.

\[5^0=1 \qquad x^0=1 \qquad \left(\frac{17}{19}\right)^0=1\]

Do you know the reason why?

Designed by Matthew Cheung. This work is licensed under a Creative Commons Attribution 4.0 International License.

- Last Updated: Nov 30, 2022 5:24 PM
- URL: https://libraryguides.centennialcollege.ca/mathhelp
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