`(1000^6)/(10^15) = ?`

Options

A. a. 10
B. b. 100
C. c. 1000
D. d. 10000

Answer

To solve the expression \((1000^6)/(10^{15})\), we can follow these steps:

### Step 1: Rewrite 1000 in terms of 10
We know that \(1000\) can be expressed as \(10^3\). Therefore, we can rewrite \(1000^6\) as:
\[ 1000^6 = (10^3)^6 \]

### Step 2: Apply the power of a power property
Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we can simplify \((10^3)^6\):
\[ (10^3)^6 = 10^{3 \cdot 6} = 10^{18} \]

### Step 3: Substitute back into the original expression
Now we can substitute \(1000^6\) back into the original expression:
\[ \frac{1000^6}{10^{15}} = \frac{10^{18}}{10^{15}} \]

### Step 4: Apply the quotient of powers property
Using the property of exponents \(\frac{a^m}{a^n} = a^{m-n}\), we can simplify the expression:
\[ \frac{10^{18}}{10^{15}} = 10^{18 - 15} = 10^3 \]

### Step 5: Calculate \(10^3\)
Finally, we calculate \(10^3\):
\[ 10^3 = 1000 \]

### Final Answer
Thus, the value of \(\frac{1000^6}{10^{15}}\) is:
\[ \boxed{1000} \]

---