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Evaluate without using a calculator. 64^-5/6

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kristenmarieb... | Student, Grade 10 | (Level 1) Valedictorian

Posted April 21, 2013 at 8:02 PM via web

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Evaluate without using a calculator. 64^-5/6

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

Posted April 21, 2013 at 8:20 PM (Answer #1)

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To simplify without a calculator, write the base (in this case 64) in its lowest form. If you cannot go straight to the prime base consider that `64 = 8 times 8 or 8^2`

We know that `8 = 2^3`  so `2^3 times 2^3 = 2^6`

`therefore 64^(-5/6)`

`= (2^6)^(-5/6)`

The rules of exponents tells us `(a^m)^n = a^(m times n)`

`therefore = 2^(-30/6)`

simplify the `30/6`

`= 2^(-5)`

Rewrite using positive exponents:

`= 1/2^5`

`= 1/32`

The answer is `2^-5`

` or 1/2^5 or 1/32` as a final answer

 

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oldnick | (Level 1) Valedictorian

Posted April 21, 2013 at 11:06 PM (Answer #2)

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`(64)^-(5/6)=1/root(6)(64^5)=1/root(6)((2^6)^5)=1/root(6)((2^5)^6)=1/2^5=1/32`

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted April 22, 2013 at 1:48 PM (Answer #3)

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We know

`64=2xx2xx2xx2xx2xx2`

`64=2^6`

`(x^m)^n=x^(mxxn)`

`Thus`

`(64)^(-5/6)=(2^6)^(-5/6)`

`(2)^(-6xx5/6)=(2)^(-5)`

`x^(-m)=1/x^n`

`2^(-5)=1/2^5`

`=1/32`

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