What is (0.23a^{-2})(-0.2b^{-3}) ?

The solution to (0.23a^{-2})(-0.2b^{-3}) is -(23)/(500a^2b^3)

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simplify (0.23a^{-2})(-0.2b^{-3})

simplify

(0.23 a^{- 2}) (- 0.2 b^{- 3})

- \frac{23}{500 a ^{2} b ^{3}}

Solution steps

(0.23 a^{- 2}) (- 0.2 b^{- 3})

Apply rule:

a (- b) = - ab

(0.23 a^{- 2}) (- 0.2 b^{- 3}) = - 0.23 a^{- 2} \cdot 0.2 b^{- 3}

= - 0.23 a^{- 2} \cdot 0.2 b^{- 3}

Multiply the numbers:

- 0.23 \cdot 0.2 = - 0.046

= - 0.046 a^{- 2} b^{- 3}

Apply exponent rule:

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

a^{- 2} = \frac{1}{a ^{2}}

= - 0.046 \cdot \frac{1}{a ^{2}} b^{- 3}

Apply exponent rule:

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

b^{- 3} = \frac{1}{b ^{3}}

= - 0.046 \cdot \frac{1}{a ^{2}} \cdot \frac{1}{b ^{3}}

Apply the fraction rule:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= - \frac{0.046 \cdot 1 \cdot 1}{a ^{2} b ^{3}}

Multiply the numbers:

0.046 \cdot 1 \cdot 1 = 0.046

= - \frac{0.046}{a ^{2} b ^{3}}

Simplify

\frac{0.046}{a ^{2} b ^{3}} : \frac{46}{1000 a ^{2} b ^{3}}

= - \frac{46}{1000 a ^{2} b ^{3}}

Cancel

- \frac{46}{1000 a ^{2} b ^{3}} : - \frac{23}{500 a ^{2} b ^{3}}

= - \frac{23}{500 a ^{2} b ^{3}}

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What is (0.23a^{-2})(-0.2b^{-3}) ?
The solution to (0.23a^{-2})(-0.2b^{-3}) is -(23)/(500a^2b^3)