Question

What is the missing exponent in the following equation?
h to the power of 450/h to the power of ? = h to the power of 215

Answer 1

To solve for the missing exponent in the equation

\[
\frac{h^{450}}{h^{?}} = h^{215},
\]

we can use the property of exponents that states

\[
\frac{a^m}{a^n} = a^{m-n}.
\]

Applying this property, we can rewrite the left side of the equation:

\[
\frac{h^{450}}{h^{?}} = h^{450 - ?}.
\]

Now we have the equation:

\[
h^{450 - ?} = h^{215}.
\]

Since the bases are the same, we can equate the exponents:

\[
450 - ? = 215.
\]

To find the value of \( ? \), we can rearrange the equation:

\[
? = 450 - 215.
\]

Calculating this gives:

\[
? = 235.
\]

Thus, the missing exponent is

\[
\boxed{235}.
\]