Question
Find the missing value for 63⋅6?=6106^{3}\cdot6^?=6^{10}6
3
⋅6
?
=6
10
. Click Here for Help Video
?=?=?=
Answers
Answered by
GPT-4o mini
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 \( 7 \).
\[
a^m \cdot a^n = a^{m+n}
\]
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 \( 7 \).
There are no human answers yet. A form for humans to post answers is coming very soon!