Q 154E - Intermediate Algebra

Question

In the following exercises, simplify:

Part (a): $q^{\frac{2}{3}}.q^{\frac{5}{6}}$

Part (b): ${\left(h^6\right)}^{\frac{4}{3}}$

Part (c): $\frac{n^{{\displaystyle \frac{3}{5}}}}{n^{{\displaystyle \frac{8}{5}}}}$

Step-by-Step Solution

Answer

Part (a): On simplifying, we get $q^{\frac{3}{2}}$.

Part (b): On simplifying, we get $h^8$.

Part (c): On simplifying, we get $\frac{1}{n}$.

Part (a) Step 1. Given information.

Consider the given question,

$q^{\frac{2}{3}}.q^{\frac{5}{6}}$

Using the product property,

$$\begin{gathered} =q^{\frac{2}{3}+\frac{5}{6}} \\ =q^{\frac{4+5}{6}} \\ =q^{\frac{9}{6}} \\ =q^{\frac{3}{2}} \end{gathered}$$

Part (b) Step 1. Given information.

Consider the given question,

${\left(h^6\right)}^{\frac{4}{3}}$

Using the power property,

$$\begin{gathered} =h^{6\times \frac{4}{3}} \\ =h^{2\times 4} \\ =h^8 \end{gathered}$$

Part (c) Step 1. Given information.

Consider the given question,

$\frac{n^{{\displaystyle \frac{3}{5}}}}{n^{{\displaystyle \frac{8}{5}}}}$

Using the quotient property,

$$\begin{gathered} =n^{\frac{3}{5}-\frac{8}{5}} \\ =n^{-\frac{5}{5}} \\ =n^{-1} \\ =\frac{1}{n} \end{gathered}$$