what is the missing number in this simplified exponential expression: 8^? dived by 8^4 = 8^15?

1 answer

To solve the expression \( \frac{8^?}{8^4} = 8^{15} \), we can use the properties of exponents.

The property states that when dividing exponential expressions with the same base, we subtract the exponents. Thus, we can rewrite the left side of the equation as follows:

\[ \frac{8^?}{8^4} = 8^{? - 4} \]

Now we can set the equation:

\[ 8^{? - 4} = 8^{15} \]

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

\[ ? - 4 = 15 \]

To find \( ? \), we can solve for it by adding 4 to both sides:

\[ ? = 15 + 4 = 19 \]

So, the missing number is:

\[ \boxed{19} \]