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

2 Answers

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

Nov 21, 2016

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