DiamondSister12
contestada

A rectangle has a length of ∛81 and a width of 3 2/3 inches. Find the area of the rectangle.

A.3 2/3 power inches squared
B.3 8/3 power inches squared
C.9 inches squared
D. 9 2/3 power inches squared

Respuesta :

First express ∛81 as an exponential expression, using the properties of exponents and roots:

[tex] \sqrt[3]{81}= 81^{ \frac{1}{3} }= (3^{4}) ^{ \frac{1}{3} }= 3^{ \frac{4}{3} } [/tex]

The area of the rectangle = length*width

=[tex]3^{ \frac{4}{3} } * 3^{ \frac{2}{3} } =3^{(\frac{4}{3} +\frac{2}{3}) }=3^{ \frac{6}{3} }= 3^{2}=9 [/tex] (inches squared).


Answer: 9 inches squared
merlynthewhizz
We have
length = ∛81
width = [tex] 3^{ \frac{2}{3} } [/tex]

Area = [tex] \sqrt[3]{81} [/tex] ×  [tex] 3^{ \frac{2}{3} } [/tex]
Area = [tex] 81^{ \frac{1}{3} } [/tex] × [tex] 3^{ \frac{2}{3} } [/tex]
Area = [tex] ( 3^{4}) ^{ \frac{1}{3} } [/tex] × [tex] 3^{ \frac{2}{3} } [/tex]
Area = [tex] 3^{ \frac{4}{3} } [/tex] × [tex] 3^{ \frac{2}{3} } [/tex]
Area = [tex] 3^{ \frac{6}{3} } [/tex]
Area = [tex] 3^{2} [/tex]
Area = 9 inches squared

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