Question

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

Answer 1

`31/4`

Explanation:

information given

• variables `\color(red)(p=4)`, `\color(blue)(q=-8)`
• equation `\color(red)(p)^(3/2)-\color(blue)(q)^(-2/3)`

concepts applied

• negative exponent `a^{-b}=1/(a^b)`
• fractional exponent `a^(b/c)=rootc{a^b} = (rootc a)^b`

calculation

• plug-in variable values
  `\color(red)(4)^(3/2)-\(color(blue)(-8)^(-2/3))`
• simplify exponents
  `\sqrt(4^3)- 1/(root3 {(8^2)})`
• simplify again
  `sqrt(64)-1/root3 64`
• simplify all roots
  `8-1/4`
• set all fractional values with equal denominators
  `32/4-1/4`

solution
`31/4`

Answer 2

`7 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

`rarr4^(3/2)-(-8^(-2/3))`

Apply the formulas

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

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

`rarrsqrt(4^3)-1/(-8^(2/3))`

`rarrsqrt(64)-1/(root(3)(-8^2))`

`rarr8-1/root(3)(64)`

`rarr8-1/4`

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