(11) $$ \left(\frac{3 x}{2} ight)^{-2} imes\left(\frac{x}{x} ight)^{2} $$

Question

(11) $$ \left(\frac{3 x}{2}ight)^{-2} 	imes\left(\frac{x}{x}ight)^{2} $$

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ (3x/2)^{-2}*(x/x)^{2} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(\frac{3x}{2}ight)^{-2}\left(\frac{x}{x}ight)^{2}$$
- step1: Divide the terms:
  $$\left(\frac{3x}{2}ight)^{-2}	imes 1^{2}$$
- step2: Evaluate the power:
  $$\left(\frac{3x}{2}ight)^{-2}	imes 1$$
- step3: Multiply:
  $$\left(\frac{3x}{2}ight)^{-2}$$
- step4: Transform the expression:
  $$\left(\frac{2}{3x}ight)^{2}$$
- step5: Rewrite the expression:
  $$\frac{2^{2}}{\left(3xight)^{2}}$$
- step6: Evaluate the power:
  $$\frac{4}{9x^{2}}$$
The simplified form of the expression $$ \left(\frac{3 x}{2}ight)^{-2} 	imes\left(\frac{x}{x}ight)^{2} $$ is $$ \frac{4}{9x^{2}} $$.
The simplified form of the expression is $$ \frac{4}{9x^{2}} $$.

(11)

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