xKingx
How do you write this in simplest form?



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xKingx
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geoffb
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\[\LARGE (b^{x})^{y} = b^{x \times y}\]

geoffb
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Remember the outside exponent also applies to the 8.

mathgirl73
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everything must be raised to 2/3 power . when raise a product by a power you multiply the exponents

xKingx
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@geoffb Can you explain how I'd use that formula with this problem?

mathgirl73
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dw:1354925885023:dw

mathgirl73
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dw:1354925885023:dw

xKingx
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Can you explain what you did in each step so I can make sure I understand it?

mathgirl73
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from the image the exponents looks negative.

xKingx
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They are

mathgirl73
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everything has to be raised by the power that is outside the parentheses. so 2/3

mathgirl73
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everything has to be raised by the power that is outside the parentheses. so 2/3

mathgirl73
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8 raised to the 2/3 and a^3 raised to the 2/3

mathgirl73
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so you have 8^2/3

mathgirl73
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you have to multiply a^3 by 2/3

mathgirl73
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so you get in the numerator 3 times 2 = 6 and the denominator 3 times 1=3

mathgirl73
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so you get in the numerator 3 times 2 = 6 and the denominator 3 times 1=3

mathgirl73
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6/3=2 so you have a^2

mathgirl73
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now you will have 8^2/3 a^2

mathgirl73
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you can't have negative exponents so you drop 82/3 down in the denominator and it becomes 8^2/3

mathgirl73
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now you have a^2/8^2/3

mathgirl73
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if you havent learned how to convert fractional exponents to radicals then you can stop there

mathgirl73
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but if not you convert 8 2/3 to a radical

mathgirl73
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dw:1354927080454:dw

xKingx
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I think I get it lol

mathgirl73
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ok

geoffb
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"you can't have negative exponents"
Sure you can. The rest of what you said looks good though.

mathgirl73
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you can but 99.9% of the time n Algebra, teachers want the answer using positive exponents.