what is the missing exponents in the following equation?

h^450/h^? = h^215

1 answer

To solve for the missing exponent in the equation \( \frac{h^{450}}{h^?} = h^{215} \), we can use the properties of exponents.

The rule for dividing exponents with the same base states that:

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

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

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

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

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

Since the bases (h) are the same, we can set the exponents equal to each other:

\[ 450 - ? = 215 \]

Now, to find the missing exponent (?), we rearrange this equation:

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

Therefore, the missing exponent is \( 235 \).