Evaluating as single power

Question

a) x⁴ ÷ x⁷

b) (1/2)^-8 (1/2)⁶

c) 3^-2x 3⁶

    _____

       3³

 

Answer 1

x⁴/x⁷ = x⁴(x^-7) = x^4-7 = x^-3 or 1/x³

 

(1/2)^-8(1/2)⁶ = (1/2)^-8+6 = (1/2)^-2

= 1/(1/2)² = 1/(1/4) = 4

 

3^-2(3⁶)/3³ = (3^-2)(3⁶)(3^-3) = 3^6-2-3 = 3¹ = 3