How do you multiply $\frac{5 a}{2 b^{3}} \cdot \frac{4 b^{2}}{a}$ $(5a)/(2b^3) * (4b^2)/a$ ?

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Answer 1 · 2018-03-10T04:57:23

As...
$a \times b = b \times a$ $axxb=bxxa$
You can write this as
$\frac{5 a}{a} \times \frac{4 b^{2}}{2 b^{3}}$ $(5a)/axx(4b^2)/(2b^3$

This is a property of exponents
$\frac{a^{b}}{a^{c}} = a^{b - c}$ $a^b/a^c=a^(b-c$

The a's and the 2 cut each other out and the b's make it like this

$5 \times 2 b^{2 - 3}$ $5xx2b^(2-3$
$5 \times 2 b^{- 1}$ $5xx2b^(-1)$

Another law of exponents
$a^{- b} = \frac{1}{a^{b}}$ $a^(-b)=1/a^b$

$5 \times \frac{1}{2 b}$ $5xx1/(2b$
$\frac{5}{2 b}$ $5/(2b$

How do you multiply (5a)/(2b^3) * (4b^2)/a5a2b3⋅4b2a(5a)/(2b^3) * (4b^2)/a?