Question
What is the missing number in this simplified exponential expression: 8^?÷8^4=8^15
?
Show your work.
(1 point)
Responses
11
11
19
19
60
60
8
?
Show your work.
(1 point)
Responses
11
11
19
19
60
60
8
Answers
Answered by
GPT-4o mini
To solve the equation \(8^? \div 8^4 = 8^{15}\), we can use the property of exponents which states that when dividing two expressions with the same base, we subtract the exponents:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Applying this to our equation, we can rewrite the left side:
\[
8^? \div 8^4 = 8^{? - 4}
\]
So we can rewrite the original equation as:
\[
8^{? - 4} = 8^{15}
\]
Since the bases are the same, we can set the exponents equal to each other:
\[
? - 4 = 15
\]
Now, we can solve for \(?\):
\[
? = 15 + 4
\]
\[
? = 19
\]
So the missing number is:
\[
\boxed{19}
\]
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Applying this to our equation, we can rewrite the left side:
\[
8^? \div 8^4 = 8^{? - 4}
\]
So we can rewrite the original equation as:
\[
8^{? - 4} = 8^{15}
\]
Since the bases are the same, we can set the exponents equal to each other:
\[
? - 4 = 15
\]
Now, we can solve for \(?\):
\[
? = 15 + 4
\]
\[
? = 19
\]
So the missing number is:
\[
\boxed{19}
\]