To solve for the missing exponent in the equation
[tex]\[
\frac{h^{450}}{h^7} = h^{215}
\][/tex]
we need to understand the properties of exponents. When you divide two expressions with the same base, you subtract the exponents. This can be written as:
[tex]\[
\frac{h^a}{h^b} = h^{a - b}
\][/tex]
Applying this property to our given equation:
[tex]\[
\frac{h^{450}}{h^7} = h^{450 - 7}
\][/tex]
Simplifying the right-hand side of the equation gives:
[tex]\[
h^{450 - 7} = h^{443}
\][/tex]
Now, we compare this result to the right-hand side of the given equation:
[tex]\[
h^{443} = h^{215}
\][/tex]
Since the bases are the same, the exponents must be equal:
[tex]\[
443 = 215
\][/tex]
However, this should lead us to realize that something is needed to balance both sides to achieve equality. We initially defined the second exponent to be \(215\), but due to this contradiction, it indicates a mistake. Thus, solving for how 443 becomes 215 is key.
By setting it up correctly:
[tex]\[
450 - 7 = 215 + \text{missing exponent}
\][/tex]
We isolate the missing exponent:
[tex]\[
450 - 7 - 215 = \text{missing exponent}
\][/tex]
Finally, solving this gives:
[tex]\[
missing \, exponent = 228
\][/tex]
Therefore, the missing exponent in the equation is:
[tex]\[
\boxed{228}
\][/tex]
