Answer:
[tex]\large \boxed{\left (\dfrac{2}{3} \right )^{8}}[/tex]
Step-by-step explanation:
Let x = the multiplier. Then
[tex]\begin{array}{rcll}x \left (\dfrac{4}{9} \right )^{-5} & = & \left (\dfrac{2}{3} \right )^{-2}&\\\\x \left [\left (\dfrac{2}{3} \right )^{2} \right ]^{-5} & = & \left (\dfrac{2}{3} \right )^{-2}&\text{Simplified }\dfrac{4}{9}\\\\x \left (\dfrac{2}{3} \right )^{-10} & = & \left (\dfrac{2}{3} \right )^{-2}&\text{ Multiplied exponents}\\\\\end{array}[/tex]
[tex]\begin{array}{rcll}x & = & \dfrac{\left (\dfrac{2}{3} \right )^{-2} }{{\left (\dfrac{2}{3} \right )^{-10}}} &\text{Divided both sides by } \left (\dfrac{2}{3} \right )^{-10}\\\\ & = & \left (\dfrac{2}{3} \right )^{8} &\text{Subtracted exponents}\\\\\end{array}\\\text{The number by which you must multiply is $\large \boxed{\mathbf{\left (\dfrac{2}{3} \right )^{8}}}$}[/tex]
