What is the value of y, if `(10)^y`= 10000000`?

Answer

To solve the equation \(10^y = 10000000\), we need to express \(10000000\) as a power of \(10\).

### Step-by-Step Solution:

1. **Identify the number**: We start with the equation:
\[ 10^y = 10000000 \]

2. **Express \(10000000\) as a power of \(10\)**: We can rewrite \(10000000\) in terms of \(10\). Notice that:
\[ 10000000 = 10,000,000 \]
We can count the number of zeros in \(10000000\). There are 7 zeros.

3. **Write \(10000000\) as \(10\) raised to a power**: Since \(10000000\) has 7 zeros, we can express it as:
\[ 10000000 = 10^7 \]

4. **Set the powers equal**: Now we have:
\[ 10^y = 10^7 \]
Since the bases are the same (both are \(10\)), we can set the exponents equal to each other:
\[ y = 7 \]

5. **Conclusion**: Therefore, the value of \(y\) is:
\[ \boxed{7} \]