Find the missing value for 6^-4 ÷ 6^? = 6^13

? =

1 answer

To solve the equation \( 6^{-4} \div 6^{?} = 6^{13} \), we can use the properties of exponents.

First, recall that dividing two powers with the same base results in subtracting the exponents:

\[ 6^{-4} \div 6^{?} = 6^{-4 - ?} \]

Now we can set the left side equal to the right side:

\[ 6^{-4 - ?} = 6^{13} \]

Since the bases are the same (both are base 6), we can set the exponents equal to each other:

\[ -4 - ? = 13 \]

Now, solve for \( ? \):

\[ -? = 13 + 4 \]

\[ -? = 17 \]

Multiply both sides by -1:

\[ ? = -17 \]

Thus, the missing value is

\[ \boxed{-17} \]