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#