Question

Somebody help!!!!! I don’t know the answer

Answer 1

Given expression

• 
  `[(\cfrac{20}{5}*\cfrac{1}{5})^(-1)]^2`

Step 1

Simplify the parenthesis:

• 
  `[(\cfrac{20}{5}*\cfrac{1}{5})^(-1)]^2=[(\cfrac{4}{5})^(-1)]^2`

Step 2

Apply the negative exponent rule:

• 
  `a^(-1)=1/a`

• 
  `[(\cfrac{4}{5})^(-1)]^2 = [(\cfrac{5}{4})^(1)]^2`

Step 3

Apply the product of a power rule:

• 
  `(a^b)^c=a^(bc)`

• 
  `(\cfrac{5}{4}})^(1*2)=(\cfrac{5}{4}})^2`

Step 4

Apply product of the product law:

• 
  `a^2=a*a`

• 
  `(\cfrac{5}{4}})^2=(\cfrac{5}{4}})^(\cfrac{5}{4}})=\cfrac{25}{16}`