Question

Find the product of -5x to the 2nd power y to the 4th power and 3xy to the 3rd power

Answer 1

Step-by-step explanation:

-5x to the 2nd powe is: (-5x)² = (-5)²x² = 25x²

y to the 4th power is: y⁴

3xy to the 3rd power is: (3xy)³ = 3³ x³ y³ = 27 x³ y³

The product of all these expressions is:

`(-5x)^2\cdot y^4\cdot(3xy)^3=25\cdot x^2\cdot y^4\cdot27\cdot x^3\cdot y^(3)`

We have to group like factors:

`(-5x)^2\cdot y^4\cdot(3xy)^3=(25\cdot27)\cdot(x^2\cdot x^3)\cdot(y^4\cdot y^(3))`

And solve

`\begin{gathered} (-5x)^2\cdot y^4\cdot(3xy)^3=(675)\cdot(x^(2+3))\cdot(y^(4+3)) \\ (-5x)^2\cdot y^4\cdot(3xy)^3=(675)\cdot(x^5)\cdot(y^7) \end{gathered}`

Answer:

The answer is 675 x⁵ y⁷