Find the missing value for 4−8⋅4?=4124^{-8}\cdot4^?=4^{12}4

Question

−8
⋅4
?
=4
12
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?=?=?=

Answer 1

To solve the equation \( 4^{-8} \cdot 4^? = 4^{12} \), we can use the properties of exponents.

The property we will use is that \( a^m \cdot a^n = a^{m+n} \). Therefore, we can combine the left side:

\[ 4^{-8} \cdot 4^? = 4^{-8 + ?} \]

Now, we set the two sides equal to each other:

\[ 4^{-8 + ?} = 4^{12} \]

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

\[ -8 + ? = 12 \]

Now, solve for \( ? \):

\[ ? = 12 + 8 = 20 \]

Thus, the missing value is

\[ ? = 20 \]