Question

Z to the power? Divided by Z to the power of seven equals Z to the power of 12 what is the?

Answer 1

To solve the equation \( \frac{Z^a}{Z^7} = Z^{12} \), we can use the properties of exponents.

1. When dividing like bases, we subtract the exponents:
\[
\frac{Z^a}{Z^7} = Z^{a - 7}
\]

2. So we rewrite the equation:
\[
Z^{a - 7} = Z^{12}
\]

3. Since the bases are the same, we can set the exponents equal to each other:
\[
a - 7 = 12
\]

4. Now, solve for \( a \):
\[
a = 12 + 7
\]
\[
a = 19
\]

So, the value of \( a \) is \( 19 \).