Evaluate Powers Expressions: (4/9)^(3/2) and (-27)^(-1/3)

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The discussion focuses on evaluating the expressions (4/9)^(3/2) and (-27)^(-1/3) as fractions. For (4/9)^(3/2), participants emphasize using the properties of exponents, particularly that a^(b/c) can be expressed as (a^b)^(1/c). For (-27)^(-1/3), the discussion clarifies that a negative exponent indicates a reciprocal, leading to the evaluation of the cube root of -27. Participants share helpful hints on manipulating exponents and roots to arrive at the correct answers. The conversation highlights the importance of understanding exponent rules for successful evaluation.
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Evalulate, leaving the answer as a fraction:


a) \left(\frac{4}{9}\right)^\frac{3}{2}


b) (-27)^-^\frac{1}{3}

Please Help.
Thanks
 
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Some useful hints:

a^\frac{b}{c} = (a^b)^\frac{1}{c} = (a^\frac{1}{c})^b

a^-^b = \frac{1}{a}^b

a^\frac{1}{b} = \sqrt<b>{a} </b>

hope that helps
 
And to add on to Imo's hints, remember that an exponent is written in the form of \frac{\mbox{power}}{\mbox{root}}

For instance, 9^{\frac{3}{2}} = (\sqrt{9})^3
 
Thank you, I finally got it. I lost my math notes and my exam is coming pretty soon so I needed to review.
 
a^-^b = \frac{1}{a^b} = \left(\frac{1}{a}\right)^b
 
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