Question

Answer the following questions below

Answer 1

Answer:

a)   $(a^{2}b)^{3} * \frac{a^{4}b}{(ab^{3})^{-1}}$

$= a^{6}b^{3} * \frac{a^{4}b}{\frac{1}{ab^{3}}}$                 ............$(x^{-z})=\frac{1}{x^{z}}$

$= a^{6}b^{3} * a^{4}b*ab^{3}$

$=(a^{6+1+4})(b^{3+1+3})$                   ............... $x^{m}*x^{n}=x^{m+n}$

$=a^{11}b^{7}$

b)   $(ab^{3})^{0}$

$=a^{0}b^{-3 * 0}$

$=a^{0}b^{0}$

= 1                        ................ $x^{0} =1$

c)   $\frac{x^{5}y^{-3}}{(x^{2}y^{2})^{2}} * (\frac{1}{xy^{2}})^{-1}$

$=\frac{\frac{x^{5}}{y^{3}}}{x^{4}y^{4}}*xy^{2}$                  .............. $(a^{-c})=\frac{1}{a^{c}}$

$=\frac{x^{5}}{y^{3} * x^{4}y^{4}}*xy^{2}$

$=\frac{(x^{5+1})y}{(y^{3+4})x^{4}}$                 ................ $a^{m}*a^{n}=a^{m+n}$

$=\frac{x^{6}y}{y^{7}x^{4}}$

$=(x^{6-4})(y^{1-7})$                 ................ $\frac{a^{m}}{a^{n}}=a^{m-n}$

$=\frac{x^{2}}{y^{6}}$                            .................. $(a^{-c})=\frac{1}{a^{c}}$

d)  $\frac{8m^{2}n}{9m^{-3}n^{2}}$ ÷ $\frac{16m^{3}n^{-1}}{3m^{4}n}$

$= \frac{8m^{2}n}{\frac{9n^{2}}{m^{3}}}$ ÷  $\frac{\frac{16m^{3}}{n}}{3m^{4}n}$                 ................... $(a^{-c})=\frac{1}{a^{c}}$

$= \frac{8m^{2}n*m^{3}}{9n^{2}}$ ÷ $\frac{16m^{3}}{3m^{4}n*n}$

$=\frac{8(m^{2+3})n}{9n^{2}}$ ÷ $\frac{16m^{3}}{3m^{4}(n^{1+1})}$         ....................... $a^{m}*a^{n}=a^{m+n}$

$=\frac{8m^{5}n}{9n^{2}}$ ÷ $\frac{16m^{3}}{3m^{4}n^{2}}$

$=\frac{8m^{5}(n^{1-2})}{9}$  ÷  $\frac{16(m^{3-4})}{3n^{2}}$                  ................... $\frac{a^{m}}{a^{n}}=a^{m-n}$

$=\frac{8m^{5}(n^{-1})}{9}$ ÷ $\frac{16(m^{-1})}{3n^{2}}$

$=\frac{8m^{5}}{9n}$ ÷  $\frac{16}{3n^{2}m}$                           ................. $(a^{-c})=\frac{1}{a^{c}}$

$=\frac{8m^{5}}{9n}*\frac{3n^{2}m}{16}$

$=\frac{(m^{5+1})(n^{2-1})}{3*2}$                      ................ $a^{m}*a^{n}=a^{m+n}$  &  $\frac{a^{m}}{a^{n}}=a^{m-n}$

$=\frac{m^{6}n}{6}$

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