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Simplify the following:$(-4)^{-3} \times 5^{-3} \times (-5)^{-3}$.
Given :
The given expression is $(-4)^{-3} \times 5^{-3} \times (-5)^{-3}$.
To do :
We have to simplify the given expression.
Solution :
$(-4)^{-3} \times 5^{-3} \times (-5)^{-3}=(-4 \times 5 \times -5)^{-3}$ $[a^m \times b^m \times c^m = (abc)^m]$
$= 100^{-3}$ $[- \times - =+]$
$= (\frac{1}{100})^3$ $[a^{-m} = (\frac{1}{a})^m]$
$= \frac{1}{100^3}$
$= \frac{1}{1000000}$
$= 0.000001$.
Therefore, the value of $(-4)^{-3} \times 5^{-3} \times (-5)^{-3}$ is 0.000001.
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