Question

Write the following in exponential form.

50 points - please show all work - thanks.

Answer 1

`\huge \boxed{ \boxed{ \red{{3}^{ (1)/(2) } {x}^{ (1)/(4) } {y}^{ - (9 )/(8) } }}}`

Explanation:

to understand this

you need to know about:

• law of exponent
• PEMDAS

given:

• 
  `\sf \sqrt[8]{81 {x}^(2) {y}^( - 9) }`

to do:

• simplification

tips and formulas:

1. 
   `\tt \sqrt[n]{x} < = > {x}^{ (1)/(n) }`
2. 
   `\displaystyle \sf( {x}^(m) {)}^(n) < = > {x}^(m n)`

let's solve:

`\sf \sqrt[8]{81 {x}^(2) {y}^( - 9) }`

`step - 2 : solve`

1. 
   `\sf rewrite \: 81 \: as \: {3}^(4) : \\ \sf\sqrt[8]{ {3}^(4) {x}^(2) {y}^( - 9) }`
2. 
   `\sf use \: {1}^(st) \: formula : \\ \sf( {3}^(4) {x}^(2) {y}^( - 9) {)}^{ (1)/(8) }`
3. 
   `\sf use \: {2}^(nd) \: formula : \\ \sf {3}^{4* (1)/(8) } * {x}^{2 * (1)/(8) } * {y}^{ - 9 * (1)/(8) }`
4. 
   `\sf \: simplify : \\ \sf {3}^{ (4)/(8) } {x}^{ (2)/(8) } {y}^{ ( - 9)/(8) } \\ \therefore \sf {3}^{ (1)/(2) } {x}^{ (1)/(4) } {y}^{ - (9 )/(8) }`

Answer 2

Given expression:

• 
  `\sqrt[8]{81x^2y^(-9)}`

Exponential form of this expression is:

• 
  `({81x^2y^(-9)})^(1/8)`

Further simplification if needed:

• 
  `({81x^2y^(-9)})^(1/8)` =
• 
  `(3^4)^(1/8)(x^2)^(1/8)(y^(-9))^(1/8)` =
• 
  `3^(1/2)x^(1/4)y^(-9/8)`