Chapter 5

For Problems \(1-30\), evaluate each numerical expression. $$ \left(-\frac{4}{3}\right)^{0} $$

For Problems \(1-40\), perform the divisions. (Objective 1) $$ \left(5 n^{2}-n-4\right) \div(n-1) $$

For Problems \(1-24\), divide the monomials. $$ \frac{65 x^{2} y^{3}}{5 x y} $$

For Problems \(9-22\), add the polynomials. $$ 3 x+4 \text { and } 5 x+7 $$

For Problems \(1-10\), find the indicated products by applying the distributive property; for example, $$ \begin{aligned} (x+1)(y+5) &=x(y)+x(5)+1(y)+1(5) \\ &=x y+5 x+y+5 \end{aligned} $$ $$ (3 x-2)(2 y-5) $$

For Problems \(1-30\), multiply using the properties of exponents to help with the manipulation. $$ \left(-3 a^{3} b\right)\left(13 a b^{2}\right) $$

For Problems \(1-30\), evaluate each numerical expression. $$ \left(-\frac{1}{2}\right)^{-3} $$

For Problems \(1-40\), perform the divisions. (Objective 1) $$ \left(7 n^{2}-61 n-90\right) \div(n-10) $$

For Problems \(1-24\), divide the monomials. $$ \frac{70 x^{3} y^{4}}{5 x^{2} y} $$

For Problems \(9-22\), add the polynomials. $$ 3 x-5 \text { and } 2 x-9 $$

For Problems \(11-36\), find the indicated products by applying the distributive property and combining similar terms. Use the following format to show your work: $$ \begin{aligned} (x+3)(x+8) &=x(x)+x(8)+3(x)+3(8) \\ &=x^{2}+8 x+3 x+24 \\ &=x^{2}+11 x+24 \end{aligned} $$ $$ (x+3)(x+7) $$

For Problems \(1-30\), multiply using the properties of exponents to help with the manipulation. $$ (-x y)\left(-5 x^{3}\right) $$

For Problems \(1-30\), evaluate each numerical expression. $$ \left(-\frac{2}{3}\right)^{-3} $$

For Problems \(1-40\), perform the divisions. (Objective 1) $$ \left(8 y^{2}+53 y-19\right) \div(y+7) $$

For Problems \(1-24\), divide the monomials. $$ \frac{-91 a^{4} b^{6}}{-13 a^{3} b^{4}} $$

For Problems \(9-22\), add the polynomials. $$ -5 y-3 \text { and } 9 y+13 $$

For Problems \(11-36\), find the indicated products by applying the distributive property and combining similar terms. Use the following format to show your work: $$ \begin{aligned} (x+3)(x+8) &=x(x)+x(8)+3(x)+3(8) \\ &=x^{2}+8 x+3 x+24 \\ &=x^{2}+11 x+24 \end{aligned} $$ $$ (x+4)(x+2) $$

For Problems \(1-30\), multiply using the properties of exponents to help with the manipulation. $$ \left(-7 y^{2}\right)\left(-x^{2} y\right) $$

For Problems \(1-30\), evaluate each numerical expression. $$ (-16)^{0} $$

For Problems \(1-40\), perform the divisions. (Objective 1) $$ \left(6 y^{2}+47 y-72\right) \div(y+9) $$

For Problems \(1-24\), divide the monomials. $$ \frac{-72 a^{5} b^{4}}{-12 a b^{2}} $$

For Problems \(9-22\), add the polynomials. $$ x^{2}-2 x-1 \text { and }-2 x^{2}+x+4 $$

For Problems \(11-36\), find the indicated products by applying the distributive property and combining similar terms. Use the following format to show your work: $$ \begin{aligned} (x+3)(x+8) &=x(x)+x(8)+3(x)+3(8) \\ &=x^{2}+8 x+3 x+24 \\ &=x^{2}+11 x+24 \end{aligned} $$ $$ (x+8)(x-3) $$

For Problems \(1-30\), multiply using the properties of exponents to help with the manipulation. $$ \left(8 a b^{2} c\right)\left(13 a^{2} c\right) $$

For Problems \(1-30\), evaluate each numerical expression. $$ (-2)^{-2} $$

For Problems \(1-40\), perform the divisions. (Objective 1) $$ \left(20 x^{2}-31 x-7\right) \div(5 x+1) $$

For Problems \(1-24\), divide the monomials. $$ \frac{18 x^{2} y^{6}}{x y^{2}} $$

For Problems \(9-22\), add the polynomials. $$ -2 x^{2}+7 x-9 \text { and } 4 x^{2}-9 x-14 $$

For Problems \(11-36\), find the indicated products by applying the distributive property and combining similar terms. Use the following format to show your work: $$ \begin{aligned} (x+3)(x+8) &=x(x)+x(8)+3(x)+3(8) \\ &=x^{2}+8 x+3 x+24 \\ &=x^{2}+11 x+24 \end{aligned} $$ $$ (x+9)(x-6) $$

For Problems \(1-30\), multiply using the properties of exponents to help with the manipulation. $$ \left(9 a b c^{3}\right)\left(14 b c^{2}\right) $$

For Problems \(1-30\), evaluate each numerical expression. $$ (-3)^{-2} $$

For Problems \(1-40\), perform the divisions. (Objective 1) $$ \left(27 x^{2}+21 x-20\right) \div(3 x+4) $$

For Problems \(1-24\), divide the monomials. $$ \frac{24 x^{3} y^{4}}{x^{2} y^{2}} $$

For Problems \(9-22\), add the polynomials. $$ 3 a^{2}+4 a-7 \text { and }-3 a^{2}-7 a+10 $$

For Problems \(11-36\), find the indicated products by applying the distributive property and combining similar terms. Use the following format to show your work: $$ \begin{aligned} (x+3)(x+8) &=x(x)+x(8)+3(x)+3(8) \\ &=x^{2}+8 x+3 x+24 \\ &=x^{2}+11 x+24 \end{aligned} $$ $$ (x-7)(x+1) $$

For Problems \(1-30\), multiply using the properties of exponents to help with the manipulation. $$ \left(5 x^{2}\right)(2 x)\left(3 x^{3}\right) $$

For Problems \(1-30\), evaluate each numerical expression. $$ -\left(3^{-2}\right) $$

For Problems \(1-40\), perform the divisions. (Objective 1) $$ \left(6 x^{2}+25 x+8\right) \div(2 x+7) $$

For Problems \(1-24\), divide the monomials. $$ \frac{32 x^{6} y^{2}}{-x} $$

For Problems \(9-22\), add the polynomials. $$ 5 x-2,3 x-7, \text { and } 9 x-10 $$

For Problems \(11-36\), find the indicated products by applying the distributive property and combining similar terms. Use the following format to show your work: $$ \begin{aligned} (x+3)(x+8) &=x(x)+x(8)+3(x)+3(8) \\ &=x^{2}+8 x+3 x+24 \\ &=x^{2}+11 x+24 \end{aligned} $$ $$ (x-10)(x+8) $$

For Problems \(1-30\), multiply using the properties of exponents to help with the manipulation. $$ (4 x)\left(2 x^{2}\right)\left(6 x^{4}\right) $$

For Problems \(1-30\), evaluate each numerical expression. $$ -\left(2^{-2}\right) $$

For Problems \(1-40\), perform the divisions. (Objective 1) $$ \left(12 x^{2}+28 x+27\right) \div(6 x+5) $$

For Problems \(1-24\), divide the monomials. $$ \frac{54 x^{5} y^{3}}{-y^{2}} $$

For Problems \(9-22\), add the polynomials. $$ -x-4,8 x+9, \text { and }-7 x-6 $$

For Problems \(11-36\), find the indicated products by applying the distributive property and combining similar terms. Use the following format to show your work: $$ \begin{aligned} (x+3)(x+8) &=x(x)+x(8)+3(x)+3(8) \\ &=x^{2}+8 x+3 x+24 \\ &=x^{2}+11 x+24 \end{aligned} $$ $$ (n-4)(n-6) $$

For Problems \(1-30\), multiply using the properties of exponents to help with the manipulation. $$ (4 x y)(-2 x)\left(7 y^{2}\right) $$

For Problems \(1-30\), evaluate each numerical expression. $$ \frac{1}{\left(\frac{3}{4}\right)^{-3}} $$

For Problems \(1-40\), perform the divisions. (Objective 1) $$ \left(2 x^{3}-x^{2}-2 x-8\right) \div(x-2) $$