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How do I solve the following math problems?

+1 vote
Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers.

1) ((a^1/6 b^-3)^3 / (x^-1y)^3) X ((x^-2 b^-1) / (a^3/2 y^1/3))

2) ((4st)^3/2 / (8s^9 t^-4)^2/3) X ((2s^-6)^-1 / (3t^1/3)^-1)
asked Feb 2, 2013 in ALGEBRA 1 by anonymous Apprentice

2 Answers

+1 vote

1).

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Arbitrary integer exponents:

                    b^{-n} = \frac{1}{b^n}  .

Identities and properties:

\begin{align}       b^{m + n} &= b^m \cdot b^n \\         (b^m)^n &= b^{m\cdot n} \\   (b \cdot c)^n &= b^n \cdot c^n \end{align}

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answered Feb 2, 2013 by richardson Scholar
+1 vote

2).

image

Arbitrary integer exponents:

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

Identities and properties:

\begin{align}       b^{m + n} &= b^m \cdot b^n \\         (b^m)^n &= b^{m\cdot n} \\   (b \cdot c)^n &= b^n \cdot c^n \end{align}

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answered Feb 2, 2013 by richardson Scholar
good explanation :)

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