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

Answer 1

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

We know that:

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

Using this property, we can rewrite the equation as:

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

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

\[ -4 - ? = 13 \]

Now, we need to solve for \( ? \):

\[ -? = 13 + 4 \] \[ -? = 17 \] \[ ? = -17 \]

Thus, the missing value is:

\[ \boxed{-17} \]