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

1 answer

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

\[ \boxed{235}. \]