simplify (2)^2/3 . (2)^1/3
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Posted by Love Rathore 5 years, 5 months ago
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Sia ? 5 years, 5 months ago
Given, {tex}2 ^ { \frac { 2 } { 3 } } \cdot 2 ^ { \frac { 1 } { 3 } }{/tex}
We know that {tex}a ^ { m } \cdot a ^ { n } = a ^ { ( m +n) }{/tex}.
So, {tex}2 ^ { \frac { 2 } { 3 } } \cdot 2 ^ { \frac { 1 } { 3 } } = ( 2 ) ^ { \frac { 2 } { 3 } + \frac { 1 } { 3 } }{/tex}
{tex}= ( 2 ) ^ { \frac { 2+1} { 3} }\\ = ( 2 ) ^ { \frac { 3 } { 3 } }\\=(2)^1\\=2{/tex}
Therefore, the value of {tex}2 ^ { \frac { 2 } { 3 } } \cdot 2 ^ { \frac { 1 } { 3 } }{/tex} will be {tex}2{/tex}.
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