Y^3Y/Y^-2

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Y^6

Move the denominator to the top..

y3Y1y+2=

y3+1+2

To simplify the expression (Y^3 * Y) / Y^(-2), we can apply the rules of exponents.

First, let's apply the rule of multiplying powers with the same base. In this case, we have Y^3 multiplied by Y^1. According to the rule, when multiplying powers with the same base, you add their exponents. So, Y^3 * Y^1 can be simplified to Y^(3+1) = Y^4.

Next, let's deal with the denominator Y^(-2). According to the rule of negative exponents, any term with a negative exponent can be moved to the opposite of the fraction and its sign reversed. So, Y^(-2) can be rewritten as 1 / Y^2.

Putting the simplified numerator and denominator together, we have Y^4 / (1 / Y^2). To divide by a fraction, we can multiply by its reciprocal. Therefore, we can rewrite the expression as Y^4 * Y^2.

Now, using the rule of multiplying powers with the same base, we add the exponents. Y^4 * Y^2 simplifies to Y^(4+2) = Y^6.

So, the final simplified expression is Y^6.