Simplify the following expression: $$ \frac{4 x^{5} y^{5}}{15} \times \frac{3 x^{3}}{12 x y} \times \frac{1}{x^{4} y} $$ $$ \frac{1}{15} x^{3} y^{3} $$ $$ \frac{12}{180} x^{3} y^{3} $$ $$ \frac{1}{15 x^{3} y^{3}} $$ $$ \frac{1}{15} x^{11} y^{3} $$ $$ \frac{1}{15 x^{11} y^{3}} $$

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UpStudy AI · Accepted Answer

First, combine the numerators and denominators:
$$
\frac{4x^5y^5}{15} \times \frac{3x^3}{12xy} \times \frac{1}{x^4y} = \frac{4x^5y^5 \cdot 3x^3 \cdot 1}{15 \cdot 12xy \cdot x^4y}.
$$

Multiply the constants:
$$
4 \times 3 = 12 \quad \text{and} \quad 15 \times 12 = 180,
$$
so the constant factor becomes $$\frac{12}{180}$$.

Combine the powers of $$x$$:
$$
x^5 \cdot x^3 = x^8 \quad \text{in the numerator, and} \quad x \cdot x^4 = x^5 \quad \text{in the denominator.}
$$

Combine the powers of $$y$$:
$$
y^5 \quad \text{in the numerator, and} \quad y \cdot y = y^2 \quad \text{in the denominator.}
$$

Thus, the expression becomes:
$$
\frac{12x^8y^5}{180x^5y^2}.
$$

Simplify the constant:
$$
\frac{12}{180} = \frac{1}{15}.
$$

Simplify the $$x$$ terms:
$$
\frac{x^8}{x^5} = x^{8-5} = x^3.
$$

Simplify the $$y$$ terms:
$$
\frac{y^5}{y^2} = y^{5-2} = y^3.
$$

Thus, the simplified expression is:
$$
\frac{1}{15} x^3y^3.
$$
The simplified expression is $$ \frac{1}{15} x^{3} y^{3} $$.

Simplify the following expression: \[ \frac{4 x^{5} y^{5}}{15} \times \frac{3 x^{3}}{12 x y} \times \frac{1}{x^{4} y} \] \( \frac{1}{15} x^{3} y^{3} \) \( \frac{12}{180} x^{3} y^{3} \) \( \frac{1}{15 x^{3} y^{3}} \) \( \frac{1}{15} x^{11} y^{3} \) \( \frac{1}{15 x^{11} y^{3}} \)

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