Problems

1. Simplify.

   (a). $\dfrac{21x^3y^2}{14x^5y}$

   (b). $\dfrac{40w^5x^4}{8wx}$

2. Simplify.

   $2u^8\cdot2w\cdot4w^3u^4$

3. Rewrite without parentheses and simplify.

   (a). $(2-y)^2$

   (b). $(5x+6)^2$

4. Simplify.

   (a). $(-9v^2+6v-5)-(-v^2-6v-6)+(-7v^2+8v+2)$

   (b). $(2w^2+3w-6)+(8w^2+3w-4)-(3w^2-3w+9)$

5. Simplify. Write your answer without using negative exponents.

   (a). $(x^{-6})^{-5}$

   (b). $(v^{-6})^3$

6. Multiply. Simplify your answer.

   $(u^2+4u+7)(2u^2-7u-3)$

7. Divide. Simplify your answer as much as possible.

   (a). $\dfrac{24z^4+12z^3-32z^2}{4z^2}$

   (b). $(27v^3+9v^2+6v)\div (-3v)$

Answer key

1. (a). $\dfrac{3y}{2x^2}$

   (b). $5w^4x^3$

2. $16u^{12}w^4$

3. (a). $4-4y+y^2$

   (b). $25x^2+60x+36$

4. (a). $-15v^2+20v+3$

   (b). $7w^2+9w-19$

5. (a). $x^{30}$

   (b). $\dfrac{1}{v^{18}}$

6. $2u^4+u^3-17u^2-61u-21$

7. (a). $6z^2+3z-8$

   (b). $-9v^2-3v-2$