Question

# How do you simplify (- 3x ^ { 3} y z ^ { 4} ) ^ { 2} ( 3y ^ { 2} z ^ { 2} )?

How do you simplify (- 3x ^ { 3} y z ^ { 4} ) ^ { 2} ( 3y ^ { 2} z ^ { 2} )?

Answer 1

${\left(- 3 {x}^{3} y {z}^{4}\right)}^{2} \left(3 {y}^{2} {z}^{2}\right) = 27 {x}^{6} {y}^{4} {z}^{10}$

#### Explanation:

Given: ${\left(- 3 {x}^{3} y {z}^{4}\right)}^{2} \left(3 {y}^{2} {z}^{2}\right)$

Watch out for expressions like this one - it is easy to miss the ${\left(\ldots\right)}^{2}$ and jump into multiplying the first term by the second.

This expression should be written out as follows as a first step:

$\left(- 3 {x}^{3} y {z}^{4}\right) \left(- 3 {x}^{3} y {z}^{4}\right) \left(3 {y}^{2} {z}^{2}\right)$

Then the expression can clearly be solved by multiplying all the numeric values, and adding all the $l i k e$ exponents.

-3*-3*3 = 27; x^3*x^3 = x^6; y*y*y^2 = y^4; z^4*z^4*z^2 = z^10 

And putting it all together:

${\left(- 3 {x}^{3} y {z}^{4}\right)}^{2} \left(3 {y}^{2} {z}^{2}\right) = 27 {x}^{6} {y}^{4} {z}^{10}$

#### Earn Coins

Coins can be redeemed for fabulous gifts.

Similar Homework Help Questions