4.4 - B. Check Up Solution

Compare your answers

Simplify the following expressions.

1.	Written Solution Video Solution $\begin{array}{rcl}(3a^{-2}{b}^{-4}{)}^{-2}& =& \frac{1}{(3a^{-2}{b}^{-4}{)}^2}\\ & =& \frac{1}{3^{1\bullet 2}{a}^{-2\bullet 2}{b}^{-4\bullet 2}}\\ & =& \frac{1}{3^2{a}^{-4}{b}^{-8}}\\ & =& \frac{a^4{b}^8}{9}\end{array}$
2.	Written Solution Video Solution $\begin{array}{rcl}\frac{(4x^{-2}{y}^{-5}{)}^{-2}}{3xy}& =& \frac{1}{3xy(4x^{-2}{y}^5{)}^2}\\ & =& \frac{1}{3xy\bullet 4^2{x}^{-2\bullet 2}{y}^{-5\bullet 2}}\\ & =& \frac{1}{3xy\bullet 16x^{-4}{y}^{-10}}\\ & =& \frac{1}{(3\bullet 16)x^{1-4}{y}^{1-10}}\\ & =& \frac{1}{48x^{-3}{y}^{-9}}\\ & =& \frac{x^3{y}^9}{48}\end{array}$
3.	Written Solution Video Solution $\begin{array}{rcl}{\left(\frac{2a^{10}{b}^{-4}}{8a^5}\right)}^{-2}& =& {\left(\frac{8a^5}{2a^{10}{b}^{-4}}\right)}^2\\ & =& \frac{8^2{a}^{5\bullet 2}}{2^2{a}^{10\bullet 2}{b}^{-4\bullet 2}}\\ & =& \frac{64a^{10}}{4a^{20}{b}^{-8}}\\ & =& \frac{64}{4}\bullet \frac{a^{10-20}}{b^{-8}}\\ & =& 16\frac{a^{-10}}{b^{-8}}\\ & =& \frac{16b^8}{a^{10}}\end{array}$
4.	Written Solution Video Solution $\begin{array}{rcl}{\left(\frac{2a^3{b}^{-2}}{3a^2{b}^{-1}}\right)}^{-3}& =& {\left(\frac{3a^2{b}^{-1}}{2a^3{b}^{-2}}\right)}^3\\ & =& \frac{3^3{a}^{2\bullet 3}{b}^{-1\bullet 3}}{2^3{a}^{3\bullet 3}{b}^{-2\bullet 3}}\\ & =& \frac{27a^6{b}^{-3}}{8a^9{b}^{-6}}\\ & =& \frac{27}{8}\bullet a^{6-9}\bullet b^{-3-(-6)}\\ & =& \frac{27}{8}\bullet a^{-3}\bullet b^3\\ & =& \frac{27b^3}{8a^3}\end{array}$