Question

By what number (4/9)-5 be multiplied so as to get (2/3)-2

Answer 1

`\large \boxed{\left ((2)/(3) \right )^(8)}`

Explanation:

Let x = the multiplier. Then

`\begin{array}{rcll}x \left ((4)/(9) \right )^(-5) & = & \left ((2)/(3) \right )^(-2)&\\\\x \left [\left ((2)/(3) \right )^(2) \right ]^(-5) & = & \left ((2)/(3) \right )^(-2)&\text{Simplified }(4)/(9)\\\\x \left ((2)/(3) \right )^(-10) & = & \left ((2)/(3) \right )^(-2)&\text{ Multiplied exponents}\\\\\end{array}`

`\begin{array}{rcll}x & = & \frac{\left ((2)/(3) \right )^(-2) }{{\left ((2)/(3) \right )^(-10)}} &\text{Divided both sides by } \left ((2)/(3) \right )^(-10)\\\\ & = & \left ((2)/(3) \right )^(8) &\text{Subtracted exponents}\\\\\end{array}\\\text{The number by which you must multiply is $\large \boxed{\mathbf{\left ((2)/(3) \right )^(8)}}$}`