Equivalent Expressions 1 — Advanced Math

Questions in this quiz (10)

1. If $$a^2b^3=12$$ and $$a^3b^2=18$$, what is the value of $$a^5b^5$$?

   • $$32$$
   • $$64$$
   • $$128$$
   • $$216$$

2. If $$x^{ac}\cdot x^{bc}=x^{30}$$, $$x$$ > $$1$$, and $$a+b=5$$, what is the value of $$c$$?

   • $$3$$
   • $$5$$
   • $$6$$
   • $$10$$

3. If $$\sqrt{x\sqrt[3]{x}}=x^a$$, then what is the value of $$a$$?

   • $$\frac{2}{3}$$
   • $$\frac{5}{6}$$
   • $$1$$
   • $$\frac{7}{6}$$

4. $$3(2x^2-5x^2y^2-4y^2)-(x^2+7x^2y^2-6y^2)$$Which of the following is equivalent to the expression above?

   • $$5x^2-22x^2y^2-6y^2$$
   • $$5x^2-8x^2y^2-6y^2$$
   • $$5x^2-22x^2y^2+6y^2$$
   • $$6x^2-22x^2y^2-6y^2$$

5. $$3(x+2)(x-5)$$Which of the following is equivalent to the expression above?

   • $$3x^2-9x-30$$
   • $$3x^2-9x+30$$
   • $$3x^2+9x-30$$
   • $$3x^2+9x+30$$

6. Which of the following is equivalent to $$9x^4-16y^2$$?

   • $$(3x^2+2y)(3x^2-8y)$$
   • $$(9x^2+4y)(x^2-4y)$$
   • $$(3x^2+4y)(3x^2-4y)$$
   • $$(9x^2-4y)(x^2+4y)$$

7. Which of the following is equivalent to the expression $$25x^4-30x^2y^2+9y^4$$?

   • $$(5x^2-3y^2)^2$$
   • $$(5x-3y)^4$$
   • $$(5x+3y)^2(5x-3y)^2$$
   • $$(25x+y)^2(x-3y)^2$$

8. $$\frac{3}{x+5}+\frac{1}{x-5}$$Which of the following is equivalent to the expression above?

   • $$\frac{4x}{(x+5)(x-5)}$$
   • $$\frac{4x-10}{(x+5)(x-5)}$$
   • $$\frac{4x+10}{(x+5)(x-5)}$$
   • $$\frac{2x}{(x+5)(x-5)}$$

9. If $$x$$ > $$2$$, which of the following is equivalent to $$\frac{x}{\frac{1}{x-2}+\frac{1}{x+2}}$$?

   • $$\frac{x^2-4}{2}$$
   • $$\frac{x^2+4}{2}$$
   • $$\frac{2x}{x^2-4}$$
   • $$\frac{x^2-4}{x}$$

10. $$(x+2)^2+2(x+2)(y-1)+(y-1)^2$$Which of the following is equivalent to the expression shown above?

    • $$(x+y+3)^2$$
    • $$(x+y+1)^2$$
    • $$(x+y)^2+1$$
    • $$(x+y)^2+x-y$$