TT Pre Algebra Lessons 91-94

Week 24:

Chapter 12

Powers, Polynomials, Radicals

Raising a number to a power

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​Lesson 91

Algebra has 6 operations (pemdas)

Repeated multiplication

The little number in the top right is the exponent. This number tells us how many times the base is multiplied by itself.

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​Exponents

Squared...

​3

​3

...and Cubed

​5

​5

​5

Multiple Choice

calculate: $$2^6$$

• 72

• 20

• 56

• 64

Multiple Choice

$$5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5$$

• $$5^8$$

• $$5^7$$

• $$5^9$$

• $$5^5$$

Multiple Choice

True or False:

Raising a number to a power is a short way to write the same number multiplied repeatedly.

• True

• False

Multiple Choice

True or False:

In a power (like $$5^3$$ ) the little number in the upper right is called the exponent and big number below is called the base.

• True

• False

Scientific notation

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Lesson 92

How are powers used in science?

Don't forget the decimal!

7,200,000,000,000,000,000.0

1. Move the decimal so that you have a number between 0 and 10.

2. Count the number of times you moved the decimal.

3. Re-write the number in scientific notation.

Multiple Choice

Rewrite in scientific notation:

83,000,000,000,000

• $$83\cdot10^{12}$$

• $$8.3\cdot10^{12}$$

• $$8.3\cdot10^{13}$$

• $$83\cdot10^{13}$$

Multiple Choice

True or False:

Scientific notation i a short way to write very large numbers that is used by scientists.

• True

• False

Multiple Choice

True or False:

Scientific notation never includes powers.

• True

• False

Match

Match the following

• $$7^2$$

• $$5^4$$

• $$8\cdot10^9$$

• $$5.7\cdot10^{13}$$

49

625

8,000,000,000

57,000,000,000,000

• 49

• 625

• 8,000,000,000

• 57,000,000,000,000

Order and powers

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​Lesson 93

Order of operations

​PEMDAS

1. All powers (exponents) are calculated first.

2. All multiplication and division are done second.

3. All addition and subtraction are third.

4. If a different order in needed, the operations that must be done first are to be placed in parentheses.

Multiple Choice

Solve:

$$\left(2\cdot3\right)^3$$

• 216

• 54

• 36

• 180

Multiple Choice

Solve:

$$\left(4+3\right)^2$$

• 59

• 25

• 13

• 49

Multiple Choice

True or False:

If they're going to be mixed with other operations, powers need to be included in the order of operations

• True

• False

Multiple Choice

True or False:

In the order of operations, powers (exponents) are done first unless parentheses indicate otherwise.

• True

• False

Adding and subtracting powers

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​Lesson 94

Adding

To add these, all we need to do is add the 3+2 because the x and the exponents are the same.

Subtracting

All we have to do is subtract the coefficients to get 3x cubed.

Multiple Choice

Simplify:

$$3x^2+4x^2$$

• $$14x$$

• $$x^2$$

• $$7x^4$$

• $$7x^2$$

Multiple Choice

calculate:

$$15-3^2$$

• 144

• 6

• 36

• 18

Reorder

Reorder the following

• Parentheses

• Exponents

• Multiplication or Division

• Addition or Subtraction

1

2

3

4

• 1
• 2
• 3
• 4

Multiple Choice

True or False:

To add x's raised to a power, you add their coefficients.

• True

• False

Multiple Choice

True or False:

Like terms are x's with the same exponents.

• True

• False

​Homework

Lessons 91-94

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