Simplify the following:$ \frac{4 a b^{2}\left(-5 a b^{3}\right)}{10 a^{2} b^{2}} $

Given:

\( \frac{4 a b^{2}\left(-5 a b^{3}\right)}{10 a^{2} b^{2}} \)

To do:

We have to simplify the given expression.

Solution:

We know that,

$(a^{m})^{n}=a^{m n}$

$a^{m} \times a^{n}=a^{m+n}$

$a^{m} \div a^{n}=a^{m-n}$

$a^{0}=1$  Therefore,

$\frac{4 a b^{2}(-5 a b^{3})}{10 a^{2} b^{2}}=\frac{4 \times(-5)}{10} \times a^{(1+1-2)} b^{(2+3-2)}$

$=-2 \times a^{0} b^{3}$

$=-2 \times 1 \times b^{3}$

$=-2 b^{3}$

Hence, $\frac{4 a b^{2}(-5 a b^{3})}{10 a^{2} b^{2}}=-2 b^{3}$. 

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Updated on: 10-Oct-2022

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