Question

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

Answer 1

Answer:

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

Step-by-step 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. $\tt \sqrt[n]{x} < = > {x}^{ \frac{1}{n} }$
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. $\sf use \: {1}^{st} \: formula : \\ \sf( {3}^{4} {x}^{2} {y}^{ - 9} {)}^{ \frac{1}{8} }$
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. $\sf \: simplify : \\ \sf {3}^{ \frac{4}{8} } {x}^{ \frac{2}{8} } {y}^{ \frac{ - 9}{8} } \\ \therefore \sf {3}^{ \frac{1}{2} } {x}^{ \frac{1}{4} } {y}^{ - \frac{9 }{8} }$

Answer 2

Answer:

Given expression:

• $\sqrt[8]{81x^2y^{-9}}$

Exponential form of this expression is:

• $({81x^2y^{-9}})^{1/8}$

Further simplification if needed:

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