Questions: y^/y^=1/y^3

y^/y^=1/y^3
Transcript text: $\frac{y^{\square}}{y^{\square}}=\frac{1}{y^{3}}$
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Solution

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Solution Steps

Step 1: Identify the given equation

The given equation is: \[ \frac{y^{\square}}{y^{\square}} = \frac{1}{y^{3}} \]

Step 2: Simplify the left-hand side

Using the property of exponents \(\frac{y^{a}}{y^{b}} = y^{a-b}\), the left-hand side simplifies to: \[ y^{\square - \square} = y^{0} \] Since \(y^{0} = 1\), the equation becomes: \[ 1 = \frac{1}{y^{3}} \]

Step 3: Solve for \(y\)

To solve for \(y\), take the reciprocal of both sides: \[ 1 = \frac{1}{y^{3}} \implies y^{3} = 1 \] Taking the cube root of both sides: \[ y = \sqrt[3]{1} = 1 \]

Final Answer

\(\boxed{y = 1}\)

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