91Ó°ÊÓ

For Problems \(31-84\), simplify each algebraic expression and express your answers using positive exponents only. $$ x^{6} x^{-1} $$

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: $$ \begin{aligned} (x+3)(x+8) &=x(x)+x(8)+3(x)+3(8) \\ &=x^{2}+8 x+3 x+24 \\ &=x^{2}+11 x+24 \end{aligned} $$ $$ (5 a+2)\left(a^{2}+a-3\right) $$

For Problems \(23-34\), subtract the polynomials using a horizontal format. $$ 3 n^{2}-7 n-9 \text { from }-4 n^{2}+6 n+10 $$

For Problems \(25-50\), perform each division of polynomials by monomials. $$ \frac{27 x^{7}-36 x^{5}-45 x^{3}}{3 x} $$

For Problems \(1-40\), perform the divisions. (Objective 1) $$ \frac{21 n^{3}+23 n^{2}-9 n-10}{3 n+2} $$

For Problems \(31-84\), simplify each algebraic expression and express your answers using positive exponents only. $$ x^{-2} x^{7} $$

For Problems \(31-46\), raise each monomial to the indicated power. Use the properties of exponents to help with the manipulation. $$ \left(3 x^{3}\right)^{2} $$

For Problems \(23-34\), subtract the polynomials using a horizontal format. $$ -4 x^{3}-x^{2}+6 x-1 \text { from }-7 x^{3}+x^{2}+6 x-12 $$

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: $$ \begin{aligned} (x+3)(x+8) &=x(x)+x(8)+3(x)+3(8) \\ &=x^{2}+8 x+3 x+24 \\ &=x^{2}+11 x+24 \end{aligned} $$ $$ \left(x^{2}+2 x+3\right)\left(x^{2}+5 x+4\right) $$

For Problems \(1-40\), perform the divisions. (Objective 1) $$ \frac{4 x^{3}+23 x^{2}-30 x+32}{x+7} $$