Name: Exponents (1.2.1) | IB DP Maths: AI HL Revision Notes 2021 Membership
Brand: Save My Exams
Price: 60 GBP
Availability: OnlineOnly
Rating: 4.7 (37 reviews)

1.2.1 Exponents

Laws of Indices

What are the laws of indices?

Laws of indices (or index laws) allow you to simplify and manipulate expressions involving exponents
- An exponent is a power that a number (called the base) is raised to
- Laws of indices can be used when the numbers are written with the same base
The index laws you need to know are:
- ${(x y)}^{m} = x^{m} y^{m}$
- ${(\frac{x}{y})}^{m} = \frac{x^{m}}{y^{m}}$
- $x^{m} \times x^{n} = x^{m + n}$
- $x^{m} \div x^{n} = x^{m - n}$
- ${(x^{m})}^{n} = x^{m n}$
- $x^{1} = x$
- $x^{0} = 1$
- $\frac{1}{x^{m}} = x^{- m}$
- $x^{\frac{1}{n}} = \sqrt[n]{x}$
- $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$
These laws are not in the formula booklet so you must remember them

How are laws of indices used?

You will need to be able to carry out multiple calculations with the laws of indices
- Take your time and apply each law individually
- Work with numbers first and then with algebra
Index laws only work with terms that have the same base, make sure you change the base of the term before using any of the index laws
- Changing the base means rewriting the number as an exponent with the base you need
- For example, $9^{4} = (3^{2})^{4} = 3^{2 \times 4} = 3^{8}$
- Using the above can them help with problems like $9^{4} \div 3^{7} = 3^{8} \div 3^{7} = 3^{1} = 3$

Worked Example

Simplify the following equations:

\frac{(3 x^{2}) (2 x^{3} y^{2})}{(6 x^{2} y)}

ai-sl-1-1-2-laws-of-indices-we-i

ii)

(4 x^{2} y^{- 4})^{3} (2 x^{3} y^{- 1})^{- 2}

Cookies

IB DP Maths: AI HL

Revision Notes

1.2.1 Exponents

Laws of Indices

What are the laws of indices?

How are laws of indices used?

Worked Example

Author: Amber

Resources

Members

Company

Quick Links