229k views
22 votes
Write the following in exponential form.

50 points - please show all work - thanks.

Write the following in exponential form. 50 points - please show all work - thanks-example-1
User MohitC
by
8.0k points

2 Answers

1 vote

Answer:


\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:


step - 1 : define


\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) }
User Yati Sawhney
by
8.6k points
6 votes

Answer:

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)
User BrunoLevy
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories