Question
Find the missing value of why to the negative power of eight times Y to the to? Power. equals Y to the 14th power what is the?
Answers
GPT-4o mini
To solve the equation \( y^{-8} \cdot y^2 = y^{14} \), we can use the laws of exponents. Specifically, we can combine the exponents on the left side.
Using the property \( y^a \cdot y^b = y^{a+b} \), we can rewrite the left side:
\[
y^{-8 + 2} = y^{14}
\]
This simplifies to:
\[
y^{-6} = y^{14}
\]
Since the bases are the same, we can set the exponents equal to each other:
\[
-6 = 14
\]
This statement is false, which indicates that there may not be a solution if we're looking for a specific value of \( y \).
However, if we are to solve for \( y \), we see that there isn't a \( y \) that satisfies this equation because \(-6\) does not equal \(14\).
In summary, this equation has no solution.
Using the property \( y^a \cdot y^b = y^{a+b} \), we can rewrite the left side:
\[
y^{-8 + 2} = y^{14}
\]
This simplifies to:
\[
y^{-6} = y^{14}
\]
Since the bases are the same, we can set the exponents equal to each other:
\[
-6 = 14
\]
This statement is false, which indicates that there may not be a solution if we're looking for a specific value of \( y \).
However, if we are to solve for \( y \), we see that there isn't a \( y \) that satisfies this equation because \(-6\) does not equal \(14\).
In summary, this equation has no solution.