## Math 6 Chapter 1 Lesson 7: Exponents with natural exponents and multiplying powers with the same base

## 1. Summary of theory Tóm

### 1.1. Powers with natural exponent.

People abbreviate 2. 2 . 2 . 2 into 2^{4} ; a . a . a to a^{3}

I call 2^{4} , a^{3} is a power

2^{4} read as 2 to 4

a^{3} read as a to the 3

The nth power of a is the product of n equal factors, each of which is equal to a : a^{n} = a . a . a . … . a ( n factors) ( n # 0)

a is called the base

n is called the exponent

Multiplication of equal factors is called raising to powers.

**VD: **

7 . 7 . 7 . 7 = 7^{4 }(read as 7 to the power of 4)

b . b . b = b^{3} (read as b to the power 3)

**Attention:** a^{2} also known as a squared (or square of a).

a^{3} also called a cube (or cube of a).

**Covenant**: a^{first} = a

### 1.2. Multiply two powers of two

**Generality: **a^{m} . a^{n} = a^{m + n}

**VD:** 2^{3} . 2^{2} = 2^{3 + 2 }= 2^{5}

a^{4 }. a^{3} = a^{4 + 3 }= a^{7}

**Attention:** When multiplying two powers with the same base, we keep the base and add the exponents.

## 2. Illustrated exercise

**Question 1:** Write the product of the following two powers into a power: x^{5} . x^{4.}

**Solution guide:**

x^{5} . x^{4} = x^{5} + 4 = x^{9}.

**Verse 2: **Shorten the following product using powers: 4. 4 . 4 . 5 . 5 . 2.

**Solution guide:**

4 . 4 . 4 . 5 . 5 . 2 = 4^{3} . 5^{2} . 2

**Question 3:** Calculate the value of the power of 2^{7}.

**Solution guide:**

2^{7} = 2 . 2 . 2 . 2 . 2 . 2 . 2 = 128.

## 3. Practice

### 3.1. Essay exercises

**Question 1:** Write the product of the following two powers to a power: x3 . x6.

**Verse 2:** Shorten the following product using powers: 3.3.3.3.7.7.9.9.9.11

**Question 3: **Calculate the value of the power 3^5.

### 3.2. Multiple choice exercises Bài

**Question 1: **Fill in the appropriate word ” …. ‘ : When multiplying two powers with the same base, we keep the base and ….. the exponents.

A. Plus

B. Minus

C. Multiply

D. Chia

**Verse 2: **16 is a power of which natural number, and what is its exponent?

A. Power of 2, exponent equals 4

B. Power of 4, exponent equals 3

C. Power of 2, exponent equals 3

D. Power of 2, exponent equals 3

**Question 3: **Do the calculation : 33 . 42

A. 423

B. 432

C. 324

D. 323

**Question 4: **Powers of 3^{4 }will equal?

A. 9

B. 27

C. 81

D. 243

**Question 5:** The cube of 7 is written as :

A. 7^{3}

B. 3^{7}

C. 7^{2}

D. 2^{7}

## 4. Conclusion

Through the lesson Exponential with natural exponents and Multiplying two powers with the same base, you need to complete some of the objectives given by the lesson such as:

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