Chapter 5: Polynomials and Polynomials Functions

In the following exercises, simplify each expression by applying several properties.

$$\begin{gathered} \left(a\right).{\left(5t^2\right)}^3{\left(3t\right)}^2 \\ \left(b\right).\frac{{\left(t^2\right)}^5{\left(t^{-4}\right)}^2}{{\left(t^3\right)}^7} \\ \left(c\right).{\left(\frac{2x{y}^2}{x^3{y}^{-2}}\right)}^2{\left(\frac{12x{y}^3}{x^3{y}^{-1}}\right)}^{-1} \end{gathered}$$

In the following exercises, simplify each expression by applying several properties.

$$\begin{gathered} \left(a\right).{\left(10k^4\right)}^3{\left(5k^6\right)}^2 \\ \left(b\right).\frac{{\left(q^3\right)}^6{\left(q^{-2}\right)}^3}{{\left(q^4\right)}^8} \end{gathered}$$

In the following exercises, simplify each expression by applying several properties.

$$\begin{gathered} \left(a\right).\left(m^2{n}^2\right){\left(2m{n}^5\right)}^4 \\ \left(b\right).\frac{{\left(-2p^{-2}\right)}^4{\left(3p^4\right)}^2}{{\left(-6p^3\right)}^2} \end{gathered}$$

In the following exercises, add or subtract the monomials.

$7x^2+5x^2+4a-9a$

In the following exercises, simplify each expression by applying several properties.

$$\begin{gathered} \left(a\right).{\left(3p{q}^4\right)}^2{\left(6p^{6}q\right)}^2 \\ \left(b\right).\frac{{\left(-2k^{-3}\right)}^2{\left(6k^2\right)}^4}{{\left(9k^4\right)}^2} \end{gathered}$$

In the following exercises, simplify each expression.

$$\begin{gathered} \left(a\right).6r^{-1} \\ \left(b\right).{\left(6r\right)}^{-1} \\ \left(c\right).{\left(-6r\right)}^{-1} \end{gathered}$$

In the following exercises, simplify each expression.

$$\begin{gathered} \left(a\right).{\left(3p\right)}^{-2} \\ \left(b\right).3p^{-2} \\ \left(c\right).-3p^{-2} \end{gathered}$$

In the following exercises, simplify each expression.

$$\begin{gathered} \left(a\right).{\left(2q\right)}^{-4} \\ \left(b\right).2q^{-4} \\ \left(c\right).-2q^{-4} \end{gathered}$$

In the following exercise, simplify each expression.

${\left(x^2\right)}^4·{\left(x^3\right)}^2$

${\left(x^2\right)}^4.{\left(x^3\right)}^2$