§8.5 Powers and Letters

C8 Powers and Letters

Mr. Fintelman (FNL)

Wednesday June 11th

2025

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C8 Powers and Letters

Mr. Fintelman (FNL)

Wednesday June 11th

2025

Slide 1 - Diapositive

Mr. Fintelman (FNL)

Wednesday November 11th

2024

Date

Wednesday June 11th 2025

Paragraph

§8.5 Powers and Letters

Pages from the handbook

Pag. 125-126

Subject

Powers and multiplications

Today is the day...

Slide 2 - Diapositive

I can already…

… calculate powers.
… calculate powers with a negative base.

Prior Knowledge

Slide 3 - Diapositive

Exercise L6 - Pag. 118

Slide 4 - Diapositive

After this lesson, I can…

… simplify the product of a power.

Goals

Slide 5 - Diapositive

Shorten expressions

2 \cdot 2 =

2 \cdot 2 \cdot 2 =

2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 =

2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 =

2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 =

Slide 6 - Diapositive

Shorten expressions

2^{​ 2 ​ ​}

2^{​ 3 ​ ​}

2^{​ 7 ​ ​}

2^{​ 12 ​ ​}

2^{​ 49 ​ ​}

Slide 7 - Diapositive

Shorten expressions - with letters

a \cdot a =

a \cdot a \cdot a =

a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a

a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a

a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a =

Slide 8 - Diapositive

Shorten expressions - with letters

a^{​ 2 ​ ​} = a \cdot a

a^{​ 3 ​ ​} = a \cdot a \cdot a

a^{​ 7 ​ ​} = a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a

a^{​ 12 ​ ​} = a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a

a^{​ 49 ​ ​} = a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a =

Slide 9 - Diapositive

Shorten expressions - with letters

a^{​ 2 ​ ​} = a \cdot a

a^{​ 2 ​ ​} b = a \cdot a \cdot b

a^{​ 4 ​ ​} b^{​ 3 ​ ​} = a \cdot a \cdot b \cdot b \cdot b \cdot a \cdot a

a^{​ 8 ​ ​} b^{​ 4 ​ ​} = a \cdot a \cdot a \cdot a \cdot b \cdot a \cdot b \cdot a \cdot b \cdot a \cdot b \cdot a

a^{​ 30 ​ ​} b^{​ 19 ​ ​} = b \cdot a \cdot b \cdot a \cdot b \cdot b \cdot a \cdot a \cdot b \cdot a \cdot a \cdot b \cdot a \cdot b \cdot a \cdot a \cdot b \cdot a \cdot a \cdot b \cdot a \cdot b \cdot a \cdot a \cdot b \cdot a \cdot a \cdot a \cdot b \cdot a \cdot a \cdot a \cdot a \cdot a \cdot b \cdot a \cdot a \cdot b \cdot b \cdot a \cdot a \cdot a \cdot b \cdot a \cdot a \cdot a \cdot b \cdot a

Slide 10 - Diapositive

Powers and multiplications

Slide 11 - Diapositive

Exercises 62 + 63 + 64 - Pag. 126

timer

6:00

Slide 12 - Diapositive

Exercise 65 - Pag. 126

Slide 13 - Diapositive

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: 62, 63, 64 and 65.

Assignments:

Pages: 125-126

Exercises: 62, 63, 64 and 65.

Assignments from the planning of §8.5:

Extra:

Exercises: 66

Slide 14 - Diapositive

Now I can…

… simplify the product of a power.

Reflection

Slide 15 - Diapositive

Mr. Fintelman (FNL)

Wednesday November 11th

2024

Date

Thursday June 12th 2025

Paragraph

§8.5 Powers and Letters

Pages from the handbook

Pag. 127-129

Subject

Sum and difference of powers

Today is the day...

Slide 16 - Diapositive

I can already…

… simplify the product of a power.

Prior Knowledge

Slide 17 - Diapositive

Exercises 62 + 63 + 64 - Pag. 126

Slide 18 - Diapositive

After this lesson, I can…

… simplify the sum and the difference of a power.

Goals

Slide 19 - Diapositive

Like terms

2 a = a + a

2 a + b = a + a + b

4 a + 3 b = a + a + b + b + b + a + a

Slide 20 - Diapositive

'Like Powers'

Slide 21 - Diapositive

'Like Powers'

Slide 22 - Diapositive

Exercises 68 + 69 - Pag. 128

timer

6:00

Slide 23 - Diapositive

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: 62, 63, 64, 65, 68, 69, 71 and 72.

Assignments:

Pages: 125-128

Exercises: 62, 63, 64, 65, 68, 69, 70, 71 and 72.

Assignments from the planning of §8.5:

Extra:

Exercises: 66 and 75.

Slide 24 - Diapositive

Now I can…

… simplify the product of a power.
… simplify the sum and the difference of a power.

Reflection

Slide 25 - Diapositive

Mr. Fintelman (FNL)

Wednesday November 11th

2024

Date

Friday June 13th 2025

Paragraph

§8.5 Powers and Letters

Pages from the handbook

Pag. 130-131

Subject

Division of powers

Today is the day...

Slide 26 - Diapositive

I can already…

… simplify the product of a power.
… simplify the sum and the difference of a power.

Prior Knowledge

Slide 27 - Diapositive

Exercise 72 - Pag. 128

Slide 28 - Diapositive

After this lesson, I can…

… simplify the division of a power.

Goals

Slide 29 - Diapositive

What do you think?

\frac{​ a ^{​ 4 ​ ​} ​ ​}{​ a ^{​ 2 ​ ​} ​} =

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

\frac{​ a ^{​ 2 ​ ​} ​ ​}{​ a ​} =

Slide 30 - Diapositive

What do you think?

\frac{​ a ^{​ 4 ​ ​} ​ ​}{​ a ^{​ 2 ​ ​} ​} = a^{​ 4 - 2 ​ ​} = a^{​ 2 ​ ​}

\frac{​ a ^{​ 4 ​ ​} b ^{​ 4 ​ ​} ​ ​}{​ a ^{​ 3 ​ ​} b ​} = a^{​ 4 - 3 ​ ​} \cdot b^{​ 4 - 1 ​ ​} = a b^{​ 3 ​ ​}

\frac{​ a ^{​ 2 ​ ​} ​ ​}{​ a ​} = a^{​ 2 - 1 ​ ​} = a^{​ 1 ​ ​} = a

Slide 31 - Diapositive

Division of powers

Slide 32 - Diapositive

Division of powers

Slide 33 - Diapositive

Exercises 78 + 79 - Pag. 130

Slide 34 - Diapositive

Exercises 80 + 81 - Pag. 130

timer

4:00

Slide 35 - Diapositive

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: 62, 63, 64, 65, 68, 69, 71, 72, 78, 79, 80, 81 and L12.

Assignments:

Pages: 125-131

Exercises: 62, 63, 64, 65, 68, 69, 70, 71, 72, 78, 79, 80, 81 and L12.

Assignments from the planning of §8.5:

Extra:

Exercises: 66, 75, 82 and 83.

Slide 36 - Diapositive

Now I can…

… simplify the product of a power.
… simplify the sum and the difference of a power.
… simplify the division of a power.

Reflection

Slide 37 - Diapositive

§8.5 Powers and Letters

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Plus de leçons comme celle-ci

§6.4 Arithmetic with Letters

§5.6 Angles in Planes

§7.4 Volume

§1.4 Simplifying Powers

§1.3 Multiplying, Adding and Subtracting Powers

§8.3 Powers

§8.1 Simplifying

Prior Knowledge