Question

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

Answer 1

Answer:

multiple is so boring I Will always say you not to post math questions

Answer 2

First, we need to convert the negative powers to positive powers. To do so we need to apply this law of exponent ⇒ $a^{-m} = \frac{1}{a^{m}}$

$(\frac{4}{9} )^{-5} = (\frac{9}{4})^{5}$

$(\frac{2}{3})^{-2} = (\frac{3}{2})^{2}$

So now our equation would be ⇒ $(\frac{9}{4})^{5} \times x = (\frac{3}{2})^{2}$

Step 1: Simplify the equation.

$(\frac{9}{4})^{5} \times x = (\frac{3}{2})^{2}$

$\frac{59049}{1024} \times x = \frac{9}{4}$

Step 2: Multiply both sides by $\frac{1024}{59049}$

$\frac{1024}{59049}\times \frac{59049}{1024} \times x =\frac{1024}{59049}\times \frac{9}{4}$

$x=\frac{256}{6561}$

∴ $\bf\frac{256}{6561}$ must be multiplies to $\bf(\frac{4}{9})^{-5}$ to obtain $\bf (\frac{2}{3})^{-2}$.