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Simplify the expression: (2^-1 + 2^-3)(8^1/3)

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rosey-girl | Student, Grade 12 | Valedictorian

Posted May 14, 2013 at 2:46 AM via web

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Simplify the expression:

(2^-1 + 2^-3)(8^1/3)

Tagged with algebra 2, math

2 Answers | Add Yours

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted May 14, 2013 at 2:56 AM (Answer #1)

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Simplify the expression `(2^(-1)+2^(-3))(8^(1/3))` :

A property of exponents is that `a^(-m)=1/a^m` so `2^(-1)=1/2` and `2^(-3)=1/2^(3)=1/8` . `1/2+1/8=4/8+1/8=5/8` , so the expression in the parantheses is `5/8` .

`8^(1/3)=root(3)(8)=2`

So we have `5/8*2=10/8=5/4`

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rakesh05 | High School Teacher | (Level 1) Assistant Educator

Posted May 14, 2013 at 6:35 AM (Answer #2)

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Given expression is  `(2^-1+2^-3)(8^(1/3))`     ........(1).

Now `2^-1=1/2`  and    `2^-3=1/2^3=1/8` .

So,     `(1/2+1/8)=4/8+1/8=5/8`

and       `(8^(1/3))=(2^3)^(1/3)=2`        As `(a^m)^n=a^(mn)` .

So,      expression (1) can be written as   

          (5/8)(2)=10/8=5/4.      Answer. 

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