Multiplying and Dividing Monomials

Multiplying and Dividing Monomials

Review: multiplying terms

Consider the following MULTIPLICATION problem:
 $3x^2\cdot2x^3$ 

Begin by MULTIPLYING the coefficients from each term.
 $3\cdot2=6$  

Review: multiplying terms

Consider the following MULTIPLICATION problem:

 $3x^2\cdot2x^3$ 

Then move from variable to variable multiplying any matching variables by ADDING their exponents.
 $x^2\cdot x^3=x^{2+3}=x^5$  

Review: multiplying terms

To complete this problem, we must multiply all of the coefficients and the variables and write them together as one term starting with the coefficient:

                $3x^2\cdot2x^3=\ ???$    

 $3\cdot2=6$  

                $x^2\cdot x^3=x^{2+3}=x^5$  

                                                $3x^2\cdot2x^3=6x^5$ 

Multiple Choice

Simplify the following expression.

 $5x^3\cdot2x^5$  

•  $10x^8$  

•  $7x^{15}$  

•  $10x^{15}$  

•  $7x^8$  

Only one number?!

The number/coefficient will not change.

Multiple Choice

Simplify the following expression.

 $3y^4\cdot y^5$  

•  $4y^{20}$  

•  $3y^{20}$  

•  $4y^9$  

•  $3y^9$  

Only one variable?!

The variable and exponent will not change.

Multiple Choice

Simplify the following expression.

 $10z^4\cdot\left(-3\right)$  

•  $7z^5$  

•  $-30z^4$  

•  $7z^4$  

•  $-30z^5$  

Multiple Choice

Simplify the following expression.

 $m^2\cdot2m^3$  

•  $2m^5$  

•  $3m^5$  

•  $2m^6$  

•  $3m^6$  

Multiple Choice

Simplify the following expression.

 $-2n\cdot8n^9$  

•  $6n^{10}$  

•  $6n^9$  

•  $-16n^{10}$  

•  $-16n^9$  

More than one variable?!

Compute each variable separately and include each variable in your answer.

Multiple Choice

Simplify the following expression.

 $4x\cdot5y$  

•  $9xy$  

•  $9x^2$  

•  $20xy$  

•  $20x^2$  

Multiple Choice

Simplify the following expression.

 $-xy\cdot-10x^2$  

•  $-11x^3y$  

•  $10x^2y$  

•  $-11x^2y$  

•  $10x^3y$  

Multiple Choice

Simplify the following expression.

 $2a^3b^4\cdot5a^{-1}b^{10}\cdot2ab$  

•  $20a^3b^{15}$  

•  $9a^{-3}b^{40}$  

•  $20a^{-3}b^{40}$  

•  $9a^3b^{15}$  

Review: dividing terms

Consider the following DIVISION problem:
 $\frac{6x^5}{3x^2}$ 

Begin by DIVIDING the coefficients from each term.
 $\frac{6}{3}=2$  

Review: dividing terms

Consider the following DIVISION problem:
 $\frac{6x^5}{3x^2}$ 

Then move from variable to variable dividing any matching variables by SUBTRTACTING their exponents
 $\frac{x^5}{x^2}=x^{5-2}=x^3$  

Review: dividing terms

To complete this problem, we must divide all of the coefficients and the variables and write them together as one term.

                $\frac{6x^5}{3x^2}=\ ???$  

 $\frac{6}{3}=2$  

                $\frac{x^5}{x^2}=x^{5-2}=x^3$  

                                               $\frac{6x^5}{3x^2}=2x^3$  

Multiple Choice

Simplify the following expression.

 $\frac{8x^6}{2x^2}$  

•  $4x^4$  
  

•  $6x^4$  

•  $4x^3$  

•  $6x^3$  

Coefficient is a fraction?!

Then your answer will also be a fraction. Put the numerator/top number on the top of the fraction and the denominator/bottom number on the bottom of the fraction.

Multiple Choice

Simplify the following expression.

 $\frac{10y^8}{4y^2}$  

•  $\frac{5y^4}{2}$  
  

•  $6x^6$  

•  $\frac{5y^6}{2}$  

•  $6x^4$  

Multiple Choice

Simplify the following expression.

 $\frac{16a^2}{2a}$  

•  $14a$  
  

•  $8a$  

•  $8a^2$  

•  $14a^2$  

Multiple Choice

Simplify the following expression.

 $\frac{3c^{12}}{9c^6}$  

•  $3c^6$  
  

•  $-6c^2$  

•  $-6c^6$  

•  $\frac{c^6}{3}$  

Negative exponents?!

Any variables with a negative exponent will end up on the numerator/bottom of the fraction.

Multiple Choice

Simplify the following expression.

 $\frac{25d^2}{15d^5}$  

•  $10d^3$  
  

•  $\frac{5}{3d^3}$  

•  $\frac{10}{d^3}$  

•  $\frac{5d^3}{3}$  

Multiple Choice

Simplify the following expression.

 $\frac{33f}{-55f^3}$  

•  $-\frac{3f^2}{5}$  
  

•  $\frac{88}{f^2}$  

•  $-\frac{3}{5f^2}$  

•  $88f^2$