## Math 6 Chapter 1 Lesson 8: Divide two powers with the same base

## 1. Summary of theory Tóm

### 1.1. For example

I know: \(5^3 . 5^4 = 5^7\)

So it can be inferred: \(5^7 : 5^3 = 5^4\) or \(5^7 : 5^4 = 5^3\)

I know: \(a^4 . a^5 = a^9\)

Therefore: \(a^9 : a^5 = a^4\) or \(a^9 : a^4 = a^5\) with a \(\ne\) 0

### 1.2. generality

We stipulate: \(a^0 = 1\) (a \(\ne\) 0)

Generality: \(a^m : a^n = a^{m – n} \)(a \(\ne\) 0 ; m \(\geq\) n)

**Attention:**

When dividing two powers with the same base (non-zero), we keep the base and subtract the exponents.

### 1.3. Attention

All natural numbers can be written as a sum of powers of 10.

**For example:** \(2475 = 2. 1000 + 4 . 100 + 7 . 10 + 5 = 2 .10^3 + 4 . 10^2 + 7 . 10 + 5 . 10^0 \)

(notice that 2 . \(10^2\) is the sum of two powers of 10 because 2 . \(10^3\) = \(10^3 + 10^3\); the same goes for the numbers 4 . \(10^2\), 7 . 10, 5 . \(10^0\)).

## 2. Illustrated exercise

**Question 1: **Write the result of the following calculation as a power: \(a^8 : a^5 \)(a \(\ne\) 0)

**Solution guide:**

\(a^8 : a^5 = a^{8 – 5} = a^3\)

**Verse 2: **Write 2437 as the sum of powers of 10

**Solution guide:**

\(2437 = 2 . 1000 + 4 . 100 + 3 . 10 + 7 = 2 . 10^3 + 4 . 10^2 + 3 . 10 + 5 . 10^0\)

** Question 3: **Do the math \(8^7 : 8^4\)

**Solution guide:**

\(8^7 : 8^4 = 8^{7 – 4} = 8^3\)

## 3. Practice

### 3.1. Essay exercises

**Question 1:** Write the result of the following calculation as a power: \(x^13 : x^8 \)(a \(\ne\) 0)

**Verse 2:** Write 71720 as the sum of powers of 10

**Question 3:** Do the math \(12^7 : 12^5\)

### 3.2. Multiple choice exercises Bài

**Question 1:** When dividing two powers with the same base (non-zero), we keep the base and … the exponents.

A. Plus

B. Minus

C. Multiply

D. Chia

**Verse 2: **The result of the calculation \(7^9 – 7^6\) as a power is:

A. \(7^5\)

B. \(7^4\)

C. \(7^3\)

D. \(7^2\)

**Question 3: **Write the number 723 as the sum of powers of 10 :

A. \(723 = 7 . 10^2 + 2 . 10 + 3 . 10^0\)

B. \(723 = 7 . 10^3 + 2 . 10^2 + 3 . 10\)

C. \(723 = 7 . 10^0 + 2 . 10 + 3 . 10^2\)

D. \(723 = 700 + 20 +3\)

**Question 4: **Where \(a^m : a^m = ?\) with a \(\ne\) 0

A. \(a^m : a^m = a\)

B. \(a^m : a^m = 1\)

C. \(a^m : a^m = 0\)

D. \(a^m – a^m = a^{2m}\)

**Question 5: **Do the calculation : \(8^7 : 8 = ?\)

A. \(8^6\)

B. \(8^5\)

C. \(8^4\)

D. \(8^3\)

## 4. Conclusion

Through this lesson Divide by two powers with the same base, you need to complete some of the objectives given by the lesson, such as:

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