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

?=

1 answer

To solve for the missing exponent in the equation \( 6^{-4} \times 6^{?} = 6^{13} \), we can use the property of exponents that states:

\[ a^m \times a^n = a^{m+n} \]

Using this property, we can combine the left side of the equation:

\[ 6^{-4} \times 6^{?} = 6^{-4 + ?} \]

So, 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:

\[ -4 + ? = 13 \]

To find \( ? \), we can solve for it:

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

Thus, the missing value is \( ? = 17 \).