Exam 2: Introduction to Algebra

Multiply: $x^{2 a} \cdot x^{a+4}$

Subtract $x^{3}-3 x^{2}+11 x$ from $4 x^{3}+x^{2}-9$ .

Raise to the power indicated: $\left(5 x y^{2}\right)^{2}$

How many terms are in the following expression? $4 x^{2}+6\left(x^{3}-3\right)$

Divide the polynomial by the binomial: $8 x^{4}-3 x^{3}+29 x^{2}-9 x+15$ by $x^{2}+3$

Write with positive exponents only: $\left(\frac{a}{5}\right)^{-2}$

Combine as indicated, and simplify: $6 a b+4 b c-2 b c-a b$

Evaluate: $\frac{x^{3 a} \cdot x^{-4}}{x}$

Raise to the power indicated: $\left(\frac{2 x y^{3}}{z^{2}}\right)^{3}$

Raise to the power indicated: $-\left(\frac{2 b}{a}\right)^{5}$

Multiply these monomials, and simplify: $(-5 x)\left(3 x y^{2} z\right)\left(-2 x^{2} z\right)\left(-x y^{3}\right)$

Simplify: $\left(x^{2 m}\right)^{n}$

Multiply the binomial and trinomial, and simplify: $\left(2 x+5 a^{2}\right)\left(4 x^{2}-10 x a^{2}+25 a^{4}\right)$

Divide the polynomial by the binomial: $3 y^{3}+5 y^{2}-8 y$ by $-y^{2}+y$

Divide: $\frac{x^a}{x^{a-7}}$

Cube this binomial: $(3 a-2)$

To maintain proper humidity, a crawl space that is $x$ metres by $2 x$ metres should have $\frac{2}{27} x^{2}(900)+$ $60[2(2 x)+2 x] \mathrm{cm}^{2}$ of ventillation. Simplify this expression. (Use fractions for the coefficients, if necessary.)

Divide $-15m^5n^2 by -7m^4$ .

Subtract $9 a^{2} b-a b^{2}-3 a b$ from $3 a b^{2}+a^{2} b+4 a b$ .

State the degree of each term. (a) $x^{5} y^{2}$ (b) $14 w x z^{2}$ (c) $-x$