$$ \frac{y^{5}}{3 w^{2}} $$ $$ 3 w^{3} y^{5} $$ $$ \frac{3 w^{4}}{y^{5}} $$ Shite the algebraic expression $$ \frac{3 x y^{-2}}{\left(w^{-1} y\right)^{3}} $$ as a equivalent expression where each variable only appear $$ \frac{3 w^{4}}{y^{6}} $$

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UpStudy AI · Accepted Answer

It looks like you're aiming to simplify the algebraic expression:

$$
\frac{3 x y^{-2}}{\left(w^{-1} y\right)^{3}}
$$

Let's break down the simplification step by step to ensure each variable only appears with positive exponents.

### Step 1: Simplify the Denominator

First, simplify the denominator $$\left(w^{-1} y\right)^{3}$$:

$$
\left(w^{-1} y\right)^{3} = w^{-3} y^{3}
$$

### Step 2: Rewrite the Original Expression

Now, substitute the simplified denominator back into the original expression:

$$
\frac{3 x y^{-2}}{w^{-3} y^{3}}
$$

### Step 3: Simplify the Fraction

To simplify the fraction, multiply the numerator and the denominator:

$$
\frac{3 x y^{-2}}{w^{-3} y^{3}} = 3 x y^{-2} \cdot w^{3} y^{-3}
$$

### Step 4: Combine Like Terms

Combine the exponents of like variables:

$$
3 x w^{3} y^{-2} y^{-3} = 3 x w^{3} y^{-5}
$$

### Step 5: Express with Positive Exponents

Convert negative exponents to positive by moving the terms to the denominator:

$$
3 x w^{3} y^{-5} = \frac{3 x w^{3}}{y^{5}}
$$

### Final Simplified Expression

$$
\frac{3 x w^{3}}{y^{5}}
$$

This is the simplified form of the original expression with all variables having positive exponents.

**Note:** It appears there might have been a miscalculation in your final expression $$\frac{3 w^{4}}{y^{6}}$$, as the variable $$x$$ should still be present in the simplified form unless additional information or constraints are provided.
The simplified expression is $$ \frac{3 x w^{3}}{y^{5}} $$.

Shite the algebraic expression as a equivalent expression where each variable only appear

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