Find the missing value forz?z6=z18\frac{z^?}{z^{6}}=z^{18}z6z?​=z18

1 answer

To solve the equation \(\frac{z^?}{z^{6}} = z^{18}\), we can use the properties of exponents.

Starting with:

\[ \frac{z^?}{z^{6}} = z^{18} \]

We can rewrite the left-hand side using the property \(\frac{a^m}{a^n} = a^{m-n}\):

\[ z^{? - 6} = z^{18} \]

Since the bases are the same, we can set the exponents equal to one another:

\[ ? - 6 = 18 \]

To find \(?\), we add 6 to both sides:

\[ ? = 18 + 6 \]

\[ ? = 24 \]

Thus, the missing value for \(?\) is \(\boxed{24}\).