Find the missing value for 6−3⋅6?=6156^{-3}\cdot6^?=6^{15}6

Question

−3
⋅6
?
=6
15
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?=?=?=

Answer 1

To solve the equation \( 6^{-3} \cdot 6^? = 6^{15} \), we can use the properties of exponents.

According to the properties of exponents, when you multiply powers with the same base, you add the exponents:

\[ 6^{-3} \cdot 6^? = 6^{-3 + ?} \]

So we can rewrite the equation as:

\[ 6^{-3 + ?} = 6^{15} \]

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

\[ -3 + ? = 15 \]

Now, we can solve for \( ? \):

\[ ? = 15 + 3 \] \[ ? = 18 \]

So, the missing value is:

\[ ? = 18 \]