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

1 answer

We start with the expression given:

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

Using the properties of exponents, particularly the property that states \(\frac{a^m}{a^n} = a^{m-n}\), we can rewrite the left side of the equation:

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

Since the bases are the same (both are base 8), we can set the exponents equal to each other:

\[ ? - 4 = 15 \]

To find the missing number (which we denote as \( ? \)), we add 4 to both sides:

\[ ? = 15 + 4 \]

Calculating that gives:

\[ ? = 19 \]

Therefore, the missing number is

\[ \boxed{19} \]