# If p-4 and q=-8 what is the value of p^(3/2)-q^(-2/3)?

##### 2 Answers
Nov 21, 2016

$\frac{31}{4}$

#### Explanation:

information given

• variables $\setminus \textcolor{red}{p = 4}$, $\setminus \textcolor{b l u e}{q = - 8}$
• equation $\setminus {\textcolor{red}{p}}^{\frac{3}{2}} - \setminus {\textcolor{b l u e}{q}}^{- \frac{2}{3}}$

concepts applied

• negative exponent ${a}^{- b} = \frac{1}{{a}^{b}}$
• fractional exponent ${a}^{\frac{b}{c}} = \sqrt[c]{{a}^{b}} = {\left(\sqrt[c]{a}\right)}^{b}$

calculation

• plug-in variable values
$\setminus {\textcolor{red}{4}}^{\frac{3}{2}} - \setminus \left({\textcolor{b l u e}{- 8}}^{- \frac{2}{3}}\right)$
• simplify exponents
$\setminus \sqrt{{4}^{3}} - \frac{1}{\sqrt[3]{\left({8}^{2}\right)}}$
• simplify again
$\sqrt{64} - \frac{1}{\sqrt[3]{64}}$
• simplify all roots
$8 - \frac{1}{4}$
• set all fractional values with equal denominators
$\frac{32}{4} - \frac{1}{4}$

solution
$\frac{31}{4}$

Nov 21, 2016

$7 \frac{3}{4}$

#### Explanation:

color(blue)(p^(3/2)-q^(-2/3)

color(orange)(p=4

color(orange)(q=-8

Let's put the variables in the equation

$\rightarrow {4}^{\frac{3}{2}} - \left(- {8}^{- \frac{2}{3}}\right)$

Apply the formulas

*color(brown)(x^(z/y)=root(y)(x^z)

*color(brown)(x^(-y)=1/(x^y)

$\rightarrow \sqrt{{4}^{3}} - \frac{1}{- {8}^{\frac{2}{3}}}$

$\rightarrow \sqrt{64} - \frac{1}{\sqrt[3]{- {8}^{2}}}$

$\rightarrow 8 - \frac{1}{\sqrt[3]{64}}$

$\rightarrow 8 - \frac{1}{4}$

color(green)(rArr31/4=7 3/4