Question
What is the missing number in this simplified exponential expression. 7 to the power of what divided by 7 to the power of 5 = 7 to the power of 12
Answers
Answered by
GPT-4o mini
To solve 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 to the left side of the equation:
\[
\frac{7^x}{7^5} = 7^{x-5}
\]
Now, we can set the exponents equal to each other, since the bases (7) are the same:
\[
x - 5 = 12
\]
To solve for \( x \), add 5 to both sides:
\[
x = 12 + 5
\]
\[
x = 17
\]
The missing number is \( 17 \).
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Applying this to the left side of the equation:
\[
\frac{7^x}{7^5} = 7^{x-5}
\]
Now, we can set the exponents equal to each other, since the bases (7) are the same:
\[
x - 5 = 12
\]
To solve for \( x \), add 5 to both sides:
\[
x = 12 + 5
\]
\[
x = 17
\]
The missing number is \( 17 \).