$$ =n $$ the power $$ 32^{7} $$, which number is the base? § Vrite'15 cubed' as a power. $$ \therefore \quad $$ Vrite these powers in expanded form. a) $$ 6^{7} $$ b) $$ 12^{5} $$ 5. Arrange these powers in ascending order of value. $$ 5^{*} ; 2^{3} ; 3^{4} ; 7^{1} ; 6^{0} $$ 5. Write this expanded form as a power. $$ 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 $$ - Determine these values. a) $$ 11^{3} $$ b) $$ 4^{4} $$ 3. Rewrite $$ 7,9 \times 10^{8} $$ in decimal notation. 9. Arrange these powers in descending order of value: $$ 3^{5} ; 5^{3} ; 9^{2} ; 4^{4} ; 136^{0} ; 2^{7} $$ - 0. Which is greater: $$ 4^{5} $$ or $$ 5^{4} $$ ? 11. In the power $$ 12^{5} $$, which number is the exponent? 12. Write these expanded forms as powers. a) $$ 3 \times 3 \times 3 \times 3 \times 5 \times 5 \times 5 $$ b) $$ 6 \times 6 \times 6 \times 6 \times 6 \times 8 \times 8 \times 8 \times 8 $$ 13. Express 86500000000 in scientific notation. 14. Convert $$ 8,013 \times 10^{8} $$ to decimal notation. 15. What is the value of $$ 365^{\prime} $$ ? 16. Write down the value of $$ 39^{\circ}-26^{\circ} $$.

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UpStudy AI · Accepted Answer

Let's break down the problem step by step.

### 1. Identify the base in $$ 32^{7} $$
In the expression $$ 32^{7} $$, the base is $$ 32 $$.

### 2. Write '15 cubed' as a power
'15 cubed' can be written as:
$$
15^{3}
$$

### 3. Expand the powers
#### a) Expand $$ 6^{7} $$
$$
6^{7} = 6 \times 6 \times 6 \times 6 \times 6 \times 6 \times 6
$$

#### b) Expand $$ 12^{5} $$
$$
12^{5} = 12 \times 12 \times 12 \times 12 \times 12
$$

### 4. Arrange the powers in ascending order of value
We need to calculate the values of the powers:
- $$ 5^{*} $$ (not defined, assuming it is $$ 5^{1} = 5 $$)
- $$ 2^{3} = 8 $$
- $$ 3^{4} = 81 $$
- $$ 7^{1} = 7 $$
- $$ 6^{0} = 1 $$

Arranging these values in ascending order:
$$
6^{0} (1), 5^{1} (5), 7^{1} (7), 2^{3} (8), 3^{4} (81)
$$

### 5. Write the expanded form as a power
The expression $$ 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 $$ can be written as:
$$
7^{7}
$$

### 6. Determine the values
#### a) Calculate $$ 11^{3} $$
$$
11^{3} = 11 \times 11 \times 11 = 1331
$$

#### b) Calculate $$ 4^{4} $$
$$
4^{4} = 4 \times 4 \times 4 \times 4 = 256
$$

### 7. Rewrite $$ 7.9 \times 10^{8} $$ in decimal notation
$$
7.9 \times 10^{8} = 790000000
$$

### 8. Arrange the powers in descending order of value
Calculating the values:
- $$ 3^{5} = 243 $$
- $$ 5^{3} = 125 $$
- $$ 9^{2} = 81 $$
- $$ 4^{4} = 256 $$
- $$ 136^{0} = 1 $$
- $$ 2^{7} = 128 $$

Arranging these values in descending order:
$$
4^{4} (256), 3^{5} (243), 5^{3} (125), 2^{7} (128), 9^{2} (81), 136^{0} (1)
$$

### 9. Which is greater: $$ 4^{5} $$ or $$ 5^{4} $$?
Calculating the values:
- $$ 4^{5} = 1024 $$
- $$ 5^{4} = 625 $$

Thus, $$ 4^{5} $$ is greater than $$ 5^{4} $$.

### 10. Identify the exponent in $$ 12^{5} $$
In the expression $$ 12^{5} $$, the exponent is $$ 5 $$.

### 11. Write the expanded forms as powers
#### a) Expand $$ 3 \times 3 \times 3 \times 3 \times 5 \times 5 \times 5 $$
This can be written as:
$$
3^{4} \times 5^{3}
$$

#### b) Expand $$ 6 \times 6 \times 6 \times 6 \times 6 \times 8 \times 8 \times 8 \times 8 $$
This can be written as:
$$
6^{5} \times 8^{4}
$$

### 12. Express $$ 86500000000 $$ in scientific notation
$$
86500000000 = 8.65 \times 10^{10}
$$

### 13. Convert $$ 8,013 \times 10^{8} $$ to decimal notation
$$
8,013 \times 10^{8} = 801300000
$$

### 14. What is the value of $$ 365^{\prime} $$?
Assuming $$ 365^{\prime} $$ refers to the number itself, the value is:
$$
365
$$

### 15. Write down the value of $$ 39^{\circ} - 26^{\circ} $$
$$
39^{\circ} - 26^{\circ} = 13^{\circ}
$$

This concludes the detailed solution to the problem.
1. The base in $$ 32^{7} $$ is 32. 2. '15 cubed' is $$ 15^{3} $$. 3. a) $$ 6^{7} = 6 \times 6 \times 6 \times 6 \times 6 \times 6 \times 6 $$ b) $$ 12^{5} = 12 \times 12 \times 12 \times 12 \times 12 $$ 4. Arranged in ascending order: $$ 6^{0} (1), 5^{1} (5), 7^{1} (7), 2^{3} (8), 3^{4} (81) $$ 5. $$ 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 = 7^{7} $$ 6. a) $$ 11^{3} = 1331 $$ b) $$ 4^{4} = 256 $$ 7. $$ 7.9 \times 10^{8} = 790000000 $$ 8. Arranged in descending order: $$ 4^{4} (256), 3^{5} (243), 5^{3} (125), 2^{7} (128), 9^{2} (81), 136^{0} (1) $$ 9. $$ 4^{5} = 1024 $$ is greater than $$ 5^{4} = 625 $$. 10. In $$ 12^{5} $$, the exponent is 5. 11. a) $$ 3 \times 3 \times 3 \times 3 \times 5 \times 5 \times 5 = 3^{4} \times 5^{3} $$ b) $$ 6 \times 6 \times 6 \times 6 \times 6 \times 8 \times 8 \times 8 \times 8 = 6^{5} \times 8^{4} $$ 12. $$ 86500000000 = 8.65 \times 10^{10} $$ 13. $$ 8,013 \times 10^{8} = 801300000 $$ 14. $$ 365^{\prime} = 365 $$ 15. $$ 39^{\circ} - 26^{\circ} = 13^{\circ} $$

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