An algebra problem by A Former Brilliant Member

Algebra Level 1

What is 9 1 / 2 9^{-1/2} × \times 2 7 1 / 3 27^{1/3} ?

1 1 9 \frac{1}{9} 9 0

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2 solutions

Andy Wong
Sep 29, 2015

9 1 / 2 = 1 9 1 / 2 = 1 9 = 1 3 27 1 / 3 = 27 3 = 3 1 3 × 3 = 1 { 9 }^{ -1/2 }\quad =\quad \frac { 1 }{ { 9 }^{ 1/2 } } \quad =\quad \frac { 1 }{ \sqrt { 9 } } \quad =\quad \frac { 1 }{ 3 } \\ \\ \\ \\{ 27 }^{ 1/3 }\quad =\quad \sqrt [ 3 ]{ 27 } \quad =\quad 3\\ \\ \\ \\\frac { 1 }{ 3 } \quad \times \quad 3\quad =\quad \boxed { 1 }

the value of 9^-1/2=1/3. Similarly value of 27^1/3=3. therefore 3 multiplied by 1/3=1

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