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tigry1 [53]
3 years ago
7

Write the following in exponential form. 50 points - please show all work - thanks.

Mathematics
2 answers:
xxMikexx [17]3 years ago
8 0

Answer:

\huge \boxed{ \boxed{ \red{{3}^{ \frac{1}{2} }  {x}^{ \frac{1}{4} }  {y}^{  - \frac{9 }{8} } }}}

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>
  • law of exponent
  • PEMDAS
<h3>given:</h3>
  • \sf  \sqrt[8]{81 {x}^{2} {y}^{ - 9}  }
<h3>to do:</h3>
  • simplification
<h3>tips and formulas:</h3>
  1. \tt   \sqrt[n]{x}  <  =  >  {x}^{ \frac{1}{n} }
  2. \displaystyle \sf( {x}^{m} {)}^{n}   <  =  >  {x}^{m  n}
<h3>let's solve:</h3>

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}  {)}^{ \frac{1}{8} }
  3. \sf use \:  {2}^{nd} \:  formula :  \\  \sf {3}^{4\times  \frac{1}{8} }  \times  {x}^{2 \times  \frac{1}{8} }  \times  {y}^{ - 9 \times  \frac{1}{8} }
  4. \sf \: simplify :  \\  \sf {3}^{ \frac{4}{8} }  {x}^{ \frac{2}{8} }  {y}^{  \frac{ - 9}{8} }  \\ \therefore  \sf  {3}^{ \frac{1}{2} }  {x}^{ \frac{1}{4} }  {y}^{  - \frac{9 }{8} }
inna [77]3 years ago
4 0

Answer:

<u>Given expression:</u>

  • <u />\sqrt[8]{81x^2y^{-9}}

<u>Exponential form of this expression is:</u>

  • <u />({81x^2y^{-9}})^{1/8}

<u>Further simplification if needed:</u>

  • <u />({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}
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