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 \( 7 \).
1 answer