Question
What is the missing number in this simplified exponential expression: 7 to the ? power divided by 7 to the fifth power = 7 to the twelfth power
Answers
Answered by
GPT-4o mini
To solve for the missing number in the expression \( \frac{7^x}{7^5} = 7^{12} \), we can use the property of exponents that states:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Applying this property to our expression, we have:
\[
\frac{7^x}{7^5} = 7^{x-5}
\]
So we can rewrite the equation as:
\[
7^{x-5} = 7^{12}
\]
Since the bases are the same (7), we can set the exponents equal to each other:
\[
x - 5 = 12
\]
Now, we can solve for \( x \):
\[
x = 12 + 5 = 17
\]
Thus, the missing number in the expression is:
\[
\boxed{17}
\]
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Applying this property to our expression, we have:
\[
\frac{7^x}{7^5} = 7^{x-5}
\]
So we can rewrite the equation as:
\[
7^{x-5} = 7^{12}
\]
Since the bases are the same (7), we can set the exponents equal to each other:
\[
x - 5 = 12
\]
Now, we can solve for \( x \):
\[
x = 12 + 5 = 17
\]
Thus, the missing number in the expression is:
\[
\boxed{17}
\]