§1.4 Simplifying Powers

C1 Arithmetic with Letters

Mr. Fintelman (FNL)

Monday September 23rd

2024

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This lesson contains 30 slides, with text slides.

Lesson duration is: 90 min

Items in this lesson

C1 Arithmetic with Letters

Mr. Fintelman (FNL)

Monday September 23rd

2024

Slide 1 - Slide

Date

Monday September 23rd 2024

Paragraph

§1.4 Simplifying Powers

Pages from the handbook

Pag. 26-28

Subject

Power of a power

Power of a product

Today is the day...

Slide 2 - Slide

I can already…

… simplify a product of powers.
… simplify a sum and a difference between powers.

Prior Knowledge

Slide 3 - Slide

Product of powers

x^{​ 2 ​ ​} \cdot x^{​ 2 ​ ​} = . . .

y^{​ 3 ​ ​} \cdot y^{​ 4 ​ ​} = . . .

3 x^{​ 2 ​ ​} \cdot 2 x^{​ 2 ​ ​} = . . .

Slide 4 - Slide

Product of powers

x^{​ 2 ​ ​} \cdot x^{​ 2 ​ ​} = x \cdot x \cdot x \cdot x = . . .

y^{​ 3 ​ ​} \cdot y^{​ 4 ​ ​} = y \cdot y \cdot y \cdot y \cdot y \cdot y \cdot y = . . .

3 x^{​ 2 ​ ​} \cdot 2 x^{​ 2 ​ ​} = 3 \cdot x \cdot x \cdot 2 \cdot x \cdot x = . . .

Slide 5 - Slide

Product of powers

x^{​ 2 ​ ​} \cdot x^{​ 2 ​ ​} = x \cdot x \cdot x \cdot x = x^{​ 4 ​ ​}

y^{​ 3 ​ ​} \cdot y^{​ 4 ​ ​} = y \cdot y \cdot y \cdot y \cdot y \cdot y \cdot y = y^{​ 7 ​ ​}

3 x^{​ 2 ​ ​} \cdot 2 x^{​ 2 ​ ​} = 3 \cdot x \cdot x \cdot 2 \cdot x \cdot x = 6 x^{​ 4 ​ ​}

Slide 6 - Slide

After this lesson, I can...

… simplify the power of a power.
… simplify the power of a product.

Goals

Slide 7 - Slide

Power of a power

(x^{​ 2 ​ ​})^{​ 2 ​ ​} = . . .

(y^{​ 4 ​ ​})^{​ 2 ​ ​} = . . .

(z^{​ 6 ​ ​})^{​ 3 ​ ​} = . . .

Slide 8 - Slide

Power of a power

(x^{​ 2 ​ ​})^{​ 2 ​ ​} = x^{​ 2 \cdot 2 ​ ​} = x^{​ 4 ​ ​}

(y^{​ 4 ​ ​})^{​ 2 ​ ​} = y^{​ 4 \cdot 2 ​ ​} = y^{​ 8 ​ ​}

(z^{​ 6 ​ ​})^{​ 3 ​ ​} = z^{​ 6 \cdot 3 ​ ​} = z^{​ 18 ​ ​}

Slide 9 - Slide

Power of a power

(x^{​ 3 ​ ​})^{​ 3 ​ ​} \cdot 2 x^{​ 2 ​ ​} = . . .

5 (z^{​ 4 ​ ​})^{​ 2 ​ ​} + 2 (z^{​ 2 ​ ​})^{​ 4 ​ ​} = . . .

Slide 10 - Slide

Power of a power

(x^{​ 3 ​ ​})^{​ 3 ​ ​} \cdot 2 x^{​ 2 ​ ​} = x^{​ 3 \cdot 3 ​ ​} \cdot 2 x^{​ 2 ​ ​} = x^{​ 6 ​ ​} \cdot 2 x^{​ 2 ​ ​} = 2 x^{​ 8 ​ ​}

5 (z^{​ 4 ​ ​})^{​ 2 ​ ​} + 2 (z^{​ 2 ​ ​})^{​ 4 ​ ​} = 5 z^{​ 4 \cdot 2 ​ ​} + 2 z^{​ 2 \cdot 4 ​ ​} =

5 z^{​ 8 ​ ​} + 2 z^{​ 8 ​ ​} = 7 z^{​ 8 ​ ​}

Slide 11 - Slide

Power of a power

Slide 12 - Slide

Power of a product

(2 x)^{​ 3 ​ ​} = . . .

(- 5 y)^{​ 3 ​ ​} = . . .

(3 a^{​ 2 ​ ​})^{​ 3 ​ ​} = . . .

Slide 13 - Slide

Power of a product

(2 x)^{​ 3 ​ ​} = 2^{​ 3 ​ ​} \cdot x^{​ 3 ​ ​} = 8 x^{​ 3 ​ ​}

(- 5 y)^{​ 3 ​ ​} = (- 5)^{​ 3 ​ ​} \cdot y^{​ 3 ​ ​} = - 125 y^{​ 3 ​ ​}

(3 a^{​ 2 ​ ​})^{​ 3 ​ ​} = 3^{​ 3 ​ ​} \cdot a^{​ 2 \cdot 3 ​ ​} = 27 a^{​ 6 ​ ​}

Slide 14 - Slide

Power of a product

Slide 15 - Slide

Worktime

You work neatly by…
… reading the theory (again) before asking a question to your classmate.
… raising a hand before asking a question to the teacher.
… if the teacher is busy, remember your question and move on.

Help:

Exercises: 51, 52, 53, 55, 57 and 58.

Assignments:

Pages: 26-28

Exercises: 51, 52, 53, 55, 57 and 58.

Assignments from the planning of WEEK 3:

Extra:

Exercises: 59

Slide 16 - Slide

Now I can...

… simplify the power of a power.
… simplify the power of a product.

Reflection

Slide 17 - Slide

Date

Wednesday September 25th 2024

Paragraph

§1.4 Simplifying Powers

Pages from the handbook

Pag. 28-30

Subject

Dividing powers

Today is the day...

Slide 18 - Slide

I can already…

… simplify the power of a power.
… simplify the power of a product.

Prior Knowledge

Slide 19 - Slide

Power of a product

(2 x)^{​ 3 ​ ​} = . . .

(- 5 y)^{​ 3 ​ ​} = . . .

(3 a^{​ 2 ​ ​})^{​ 3 ​ ​} = . . .

Slide 20 - Slide

Power of a product

(2 x)^{​ 3 ​ ​} = 2^{​ 3 ​ ​} \cdot x^{​ 3 ​ ​} = 8 x^{​ 3 ​ ​}

(- 5 y)^{​ 3 ​ ​} = (- 5)^{​ 3 ​ ​} \cdot y^{​ 3 ​ ​} = - 125 y^{​ 3 ​ ​}

(3 a^{​ 2 ​ ​})^{​ 3 ​ ​} = 3^{​ 3 ​ ​} \cdot a^{​ 2 \cdot 3 ​ ​} = 27 a^{​ 6 ​ ​}

Slide 21 - Slide

After this lesson, I can...

… simplify the division of powers.

Goals

Slide 22 - Slide

Dividing powers

\frac{​ 6 a ​ ​}{​ a ​} = . . .

\frac{​ 8 a b ​ ​}{​ 2 b ​} = . . .

\frac{​ a ^{​ 2 ​ ​} b ​ ​}{​ a b c ​} = . . .

Slide 23 - Slide

Dividing powers

\frac{​ 6 a ​ ​}{​ a ​} = \frac{​ 6 \cdot a ​ ​}{​ a ​} = 6

\frac{​ 8 a b ​ ​}{​ 2 b ​} = \frac{​ 8 \cdot a \cdot b ​ ​}{​ 2 \cdot b ​} = 4 a

\frac{​ a ^{​ 2 ​ ​} b ​ ​}{​ a b c ​} = \frac{​ a \cdot a \cdot b ​ ​}{​ a \cdot b \cdot c ​} = \frac{​ a ​ ​}{​ c ​}

Explanation

Dividing variables works similarly to dividing regular numbers. To divide variables, pay attention to which variables are in the numerator and denominator.

For example, if you have 6/𝑎, both parts of the fraction have the variable 'a' in them. Thus, you can divide it by 'a'.

Slide 24 - Slide

Dividing powers

\frac{​ a ^{​ 7 ​ ​} ​ ​}{​ a ^{​ 3 ​ ​} ​} = . . .

\frac{​ x ^{​ 5 ​ ​} ​ ​}{​ x ^{​ 3 ​ ​} ​} = . . .

\frac{​ 5 a ^{​ 8 ​ ​} b ^{​ 2 ​ ​} ​ ​}{​ 2 5 a ^{​ 3 ​ ​} b ​} = . . .

Slide 25 - Slide

Dividing powers

\frac{​ a ^{​ 7 ​ ​} ​ ​}{​ a ^{​ 3 ​ ​} ​} = \frac{​ a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a ​ ​}{​ a \cdot a \cdot a ​} = a^{​ 4 ​ ​}

\frac{​ x ^{​ 5 ​ ​} ​ ​}{​ x ^{​ 3 ​ ​} ​} = \frac{​ x \cdot x \cdot x \cdot x \cdot x ​ ​}{​ x \cdot x \cdot x ​} = x^{​ 2 ​ ​}

\frac{​ 5 a ^{​ 8 ​ ​} b ^{​ 2 ​ ​} ​ ​}{​ 2 5 a ^{​ 3 ​ ​} b ​} = \frac{​ 5 \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot b \cdot b ​ ​}{​ 5 \cdot 5 \cdot a \cdot a \cdot a \cdot b ​} = \frac{​ a ^{​ 5 ​ ​} b ​ ​}{​ 5 ​}

Explanation

If you have trouble dividing variables, try writing down all the factors in both the numerator and denominator. This way, you can remove the variables more carefully. It may take some time to write everything down, but it is not required for the test or any official purposes.

Slide 26 - Slide

Dividing powers - 'According to the book'

\frac{​ a ^{​ 7 ​ ​} ​ ​}{​ a ^{​ 3 ​ ​} ​} = a^{​ 4 ​ ​}

\frac{​ x ^{​ 5 ​ ​} ​ ​}{​ x ^{​ 3 ​ ​} ​} = x^{​ 2 ​ ​}

\frac{​ 5 a ^{​ 8 ​ ​} b ^{​ 2 ​ ​} ​ ​}{​ 2 5 a ^{​ 3 ​ ​} b ​} = \frac{​ a ^{​ 5 ​ ​} b ​ ​}{​ 5 ​}

Slide 27 - Slide

Dividing powers

Slide 28 - Slide

Worktime

You work neatly by…
… reading the theory (again) before asking a question to your classmate.
… raising a hand before asking a question to the teacher.
… if the teacher is busy, remember your question and move on.

Help:

Exercises: 60, 61 and 63.

Assignments:

Pages: 28-30

Exercises: 60, 61 and 63.

Assignments from the planning of WEEK 3:

Extra:

Exercises: -

Slide 29 - Slide

Now I can...

… simplify the division of powers.

Reflection

Slide 30 - Slide

§1.4 Simplifying Powers

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