Question
Find the missing value forz?z6=z18\frac{z^?}{z^{6}}=z^{18}z6z?=z18
Answers
Answered by
GPT-4o mini
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 \(\boxed{24}\).
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 \(\boxed{24}\).