Question

Which expression is equivalent to (xy^-6)^2 for all values of x and y where the expression is defined?

A. xy^-36
B. xy^ 36
C. x^2y^ -12
D. x^2y^ 12

Answer 1

`\huge \boxed{ \boxed{ \mathbb{C)} {x}^(2) {y}^( - 12) }}`

Explanation:

to understand this

you need to know about:

• law of exponent
• PEMDAS

tips and formulas:

• 
  `\sf( {x}^(m) {)}^(n) < = > {x}^(mn)`
• 
  `\sf x < = > {x}^(1)`

let's solve:

`{(xy}^( - 6) ) ^(2)`

1. 
   `\sf \: use \: 1st \: and \: 2nd \: formula : \\ ( {x}^(1 * 2) {y}^( - 6 * 2) )`
2. 
   `\sf simplify : \\ {x}^(2) {y}^( - 12)`

Answer 2

C.

First, you square the x because it is inside the parentheses. Then, you multiply the -6 by 2, to get your exponent of -12 for the y.