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Mathematics for Technology II (Math 2131)

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Study Force Academy
Durham College, Mathematics
Free
  • 36 lessons
  • 0 quizzes
  • 14 week duration

Review of the Exponent Laws

Radicals (√, ∛, ∜, etc.) are an extension of the exponents laws you learned in Part 1 of this course. This section is solely dedicated to the exponent laws. The connection between radicals and exponents is made in the next section, though it’s highly advised that you review these first as they’re easily forgettable! A summary of the rules are outlined below with examples.

Product rule:

Rule:

xa·xb=xa+b

Examples:

y2y4=y6bb3b4=b8

You try:

m3mn

Answer:

m3+n

(notice how the exponent 3 and n are not like terms so we leave it as 3 + n.

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Quotient rule:

Rule:

xaxb=xab

Examples:

y5y2=y3x2y5xy3=xy2

You try:

a5na2n

Answer:

a3n

(notice how the exponents 5n and 2n are like terms, so we subtract the coefficients only).

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Power of a power rule:

Rule:

xab=xa×b

Examples:

x25=x10xy4=x4y4

Test:

3y3

Answer:

27y3

(Students will commonly mistaken the power with multiplication, for example, multiply the exponent 3 by the base 3 instead of 3 × 3 × 3 = 27)

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A thorough explanation of these laws and more are provided in the video:

Common error:

x+ynxn+yn

Students of all math backgrounds make this common mistake. Remember, you can only distribute the exponent n if what’s inside the brackets is a monomial; x and y are two separate terms, hence a binomial. You could distribute the n in the following cases:

xynxnynxx+ynxnx+yn

In the lesson to come, you will learn how to handle expressions like (x + y)² via a technique called expanding. For a list of other common math errors, watch this link.


Now it’s time to put your knowledge of exponents to the test. The video below shows three complicated examples that require you use several of the exponent laws to simplify a single expression.

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