Question

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

Answer 1

To solve the equation \( \frac{h^{450}}{h} = h^{215} \), we can simplify the left side using the property of exponents which states that \( \frac{a^m}{a^n} = a^{m-n} \).

Applying this to the left side:

\[
\frac{h^{450}}{h} = h^{450 - 1} = h^{449}
\]

Now, we set this equal to the right side of the equation:

\[
h^{449} = h^{215}
\]

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

\[
449 = 215
\]

Clearly, this is not correct, indicating we should solve for the missing exponent. The equation was intended to represent:

\[
h^{450 - x} = h^{215}
\]

Where \( x \) is the exponent that we need to find. So we equate the exponents:

\[
450 - x = 215
\]

Solving for \( x \):

\[
x = 450 - 215
\]
\[
x = 235
\]

Thus, the missing exponent is \( \boxed{235} \).