Question
Fill in the box so that the statement is true. Assume that all bases are not equal to 0 . \( y^{[]}=\frac{1}{y^{6}} \)
Ask by Mitchell Thornton. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The missing exponent is \(-6\).
Solution
Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.
Unlock
Reviewed and approved by the UpStudy tutoring team
Like
The Deep Dive
To solve for the empty box in the equation \( y^{[]} = \frac{1}{y^{6}} \), we need to use the properties of exponents. The term \( \frac{1}{y^{6}} \) can be rewritten as \( y^{-6} \). Therefore, the equation can be updated to \( y^{[]} = y^{-6} \). This means that the exponent in the empty box must be \(-6\). So, we have \( y^{-6} = \frac{1}{y^{6}} \). Thus, the final answer is: \( y^{-6}=\frac{1}{y^{6}} \)