Question

Solve: (y?)4=y−8\left(y^?\right)^{4}=y^{-8}(y
?
)
4
=y
−8

Answer 1

To solve the equation \((y^?)^4 = y^{-8}\), we can start by simplifying both sides.

1. Rewrite the left side: \((y^?)^4\) means raising \(y^?\) to the fourth power.
2. The right side, \(y^{-8}\), indicates \(y\) raised to the power of \(-8\) or \(\frac{1}{y^{8}}\).

Now the equation can be rewritten as:

\[
(y^?)^4 = \frac{1}{y^8}
\]

Taking the fourth root of both sides, we get:

\[
y^? = \left(\frac{1}{y^8}\right)^{1/4}
\]

This simplifies to:

\[
y^? = y^{-2}
\]

Now we exponentiate both sides. Since \(y^? = y^{-2}\):

1. If we assume the unknown exponent \(?\) is being represented, we can equate the exponents since the bases (both are \(y\)) are the same.

Thus, we have:

\[
? = -2
\]

So the solution to the equation \((y^?)^4 = y^{-8}\) yields:

\[
? = -2
\]