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How do the laws work with rational exponents?

Laws of exponents? Please help?

  • I have this one math problem that I just can't seem to figure out.. The question says: Use the laws of exponents to simplify. Do not use negative exponents in the answer. Assume that even roots are of non-negative quantities and that all denominators are non-zeros. (9k^2 m^-4)1/2 Can anyone please explain how to do this? I promise to give 11 points (best answer and thumbs up) to whoever can help me. :\

  • Answer:

    Sure, the ½ power is also √ . To take the square root of a power, you halve the power. √9 =3. √k² = k and √m⁻ᶣ = m⁻². So (9k²m⁻ᶣ)^½ = 3km⁻² You can also write this as 3k/m²

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When you have a negative exponent on the top line, put it underneath the line as a positive exponent. This rule works the other way around too. If there's a negative exponent on the bottom, write it on top as a positive exponent. (9k^2 m^-4)/2 (9k^2) / [(2)(m^4)] (9k^2) / (2m^4)

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