Question

Simplify the given expression.

$\left(2xy\right)\left(-3x^2{y}^5\right)$

Short answer

The final expression is $-6x^3{y}^6$.

Step-by-step solution

Step 1. Define an expression.

A mathematical expression is a combinations of numbers and variables ordered with mathematical operations.

Step 2. Define the meaning of power of a product rule.

Power of a product rule states that if the two exponents of the same base are multiplied then the exponents are added and base remains the same.

$a^m.a^n=a^{m+n}$

Where,$a$ is any non-zero real number.

Step 3. Simplify the expression 2xy−3x2y5.

Use the power of a product rule to simplify the given expression.

$$\begin{gathered} \left(2xy\right)\left(-3x^2{y}^5\right)=\left(2\right)\left(x\right)\left(y\right)\left(-3\right)\left(x^2\right)\left(y^5\right) \\ =\left(2\right)\left(-3\right)\left(x\right)\left(x^2\right)\left(y\right)\left(y^5\right) \\ =-6\left(x^{1+2}\right)\left(y^{1+5}\right) \\ =-6x^3{y}^6 \end{gathered}$$

Hence, $\left(2xy\right)\left(-3x^2{y}^5\right)=-6x^3{y}^6$.

Therefore the final expression is $-6x^3{y}^6$.