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Multiply. Simplify your answer. $\newline$ $\frac{4z^2}{10z^2} \times 8z^2$

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Multiply and divide rational expressions

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Q. Multiply. Simplify your answer.

\newline

\frac{4z^2}{10z^2} \times 8z^2

Identify Terms: Identify the terms to be multiplied and rewrite the multiplication expression. $\newline$ We have the fraction $\frac{4z^2}{10z^2}$ and we want to multiply it by $8z^2$ . The multiplication expression is $\left(\frac{4z^2}{10z^2}\right) \times 8z^2$ .
Simplify Fraction: Simplify the fraction before multiplying. $\newline$ The $z^2$ terms in the numerator and denominator of the fraction $\frac{4z^2}{10z^2}$ cancel each other out because they are the same, leaving us with $\frac{4}{10}$ . This simplification is valid because $\frac{z^2}{z^2} = 1$ , provided that $z$ is not equal to zero.
Further Simplify: Further simplify the fraction $\frac{4}{10}$ . The fraction $\frac{4}{10}$ can be reduced by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . This gives us $\frac{2}{5}$ .
Multiply Fraction: Multiply the simplified fraction by $8z^2$ . Now we multiply the simplified fraction $\frac{2}{5}$ by $8z^2$ . This gives us $(\frac{2}{5}) * 8z^2$ .
Perform Multiplication: Perform the multiplication. $\newline$ Multiplying $\frac{2}{5}$ by $8z^2$ , we get $2 \times 8z^2 / 5$ , which simplifies to $\frac{16z^2}{5}$ .
Write Final Answer: Write the final answer in simplest form. $\newline$ The final simplified result of the multiplication is $\frac{16z^2}{5}$ , which is already in its simplest form.

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