Exponents problem

Algebra Level 1

Evaluate 1 6 0.125 − ( 0.5 ) − 0.5 \large 16^{0.125} - (0.5)^{-0.5}


The answer is 0.

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Irvan Ary Maulana Nugroho by Irvan Ary Maulana Nugroho , 20

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2 solutions

1 6 0.125 − ( 0.5 ) − 0.5 = 2 4 × 0.125 − 2 ( − 1 ) × ( − 0.5 ) 16^{0.125}-(0.5)^{-0.5} = 2^{4 \times 0.125}-2^{(-1) \times (-0.5)}

= 2 0.5 − 2 0.5 = 0 =2^{0.5}-2^{0.5}=0

33 Helpful 4 Interesting 9 Brilliant 2 Confused

Thats one of the more elegant easy to read and understand solutions, an ahah! moment :)

John McLachlan - 3 years, 6 months ago

where does the -1 come from in the second term as an exponent ?

William Rothamel - 2 years, 8 months ago

1 6 0.125 − ( 0.5 ) − 0.5 = 1 6 1 8 − ( 1 2 ) − 1 2 = 2 4 × 1 8 − ( 2 − 1 ) − 1 2 = 2 1 2 − 2 1 2 = 0 16^{0.125} - (0.5)^{-0.5} = 16^{\frac {1}{8}} - (\frac {1}{2})^{-\frac {1}{2}} = 2^{4 \times \frac {1}{8}} - (2^{-1})^{-\frac {1}{2}} = 2^{\frac {1}{2}} - 2^{\frac {1}{2}} = \boxed{0}

10 Helpful 0 Interesting 3 Brilliant 0 Confused

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