`(1000)^(7)div10^(18)=?`

Options

A. 10
B. 100
C. 1000
D. 10000

Answer

To solve the expression \((1000)^{7} \div (10)^{18}\), we can follow these steps:

### Step 1: Rewrite 1000 in terms of powers of 10
We know that:
\[ 1000 = 10^3 \]
So we can rewrite the expression as:
\[ (10^3)^{7} \div (10^{18}) \]

### Step 2: Apply the power of a power rule
Using the rule \((a^m)^n = a^{m \cdot n}\), we can simplify \((10^3)^{7}\):
\[ (10^3)^{7} = 10^{3 \cdot 7} = 10^{21} \]
Now our expression becomes:
\[ 10^{21} \div 10^{18} \]

### Step 3: Apply the quotient of powers rule
Using the rule \(\frac{a^m}{a^n} = a^{m-n}\), we can simplify:
\[ 10^{21} \div 10^{18} = 10^{21 - 18} = 10^{3} \]

### Step 4: Calculate the final result
Now we can evaluate \(10^{3}\):
\[ 10^{3} = 1000 \]

### Final Answer
Thus, the value of \((1000)^{7} \div (10)^{18}\) is:
\[ \boxed{1000} \]