Find the missing value for 63⋅6?=6106^{3}\cdot6^?=6^{10}6

3
⋅6
?
=6
10
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1 answer

To solve for the missing exponent \( ? \) in the equation \( 6^3 \cdot 6^? = 6^{10} \), we can use the property of exponents that states:

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

Applying this to our equation, we have:

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

So we can rewrite the equation as:

\[ 6^{3+?} = 6^{10} \]

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

\[ 3 + ? = 10 \]

Now, we solve for \( ? \):

\[ ? = 10 - 3 \] \[ ? = 7 \]

The missing value is \( 7 \).