Solve {left(50*60/50+60right)}^2left(1/50^20.3+1/60^2-0.2right)

$${ \left( \frac{ 50 \cdot 60 }{ 50+60 } \right) }^{ 2 } \left( \frac{ 1 }{ { 50 }^{ 2 } } 0.3+ \frac{ 1 }{ { 60 }^{ 2 } } -0.2 \right)$$

Evaluate

$$-\frac{89821}{605}\approx -148.46446281$$

Solution Steps

Multiply 50 and 60 to get 3000.

$$\left(\frac{3000}{50+60}\right)^{2}\left(\frac{1}{50^{2}}\times 0.3+\frac{1}{60^{2}}-0.2\right)$$

Add 50 and 60 to get 110.

$$\left(\frac{3000}{110}\right)^{2}\left(\frac{1}{50^{2}}\times 0.3+\frac{1}{60^{2}}-0.2\right)$$

Reduce the fraction \frac{3000}{110} to lowest terms by extracting and canceling out 10.

$$\left(\frac{300}{11}\right)^{2}\left(\frac{1}{50^{2}}\times 0.3+\frac{1}{60^{2}}-0.2\right)$$

Calculate \frac{300}{11} to the power of 2 and get \frac{90000}{121}.

$$\frac{90000}{121}\left(\frac{1}{50^{2}}\times 0.3+\frac{1}{60^{2}}-0.2\right)$$

Calculate 50 to the power of 2 and get 2500.

$$\frac{90000}{121}\left(\frac{1}{2500}\times 0.3+\frac{1}{60^{2}}-0.2\right)$$

Multiply \frac{1}{2500} and 0.3 to get \frac{3}{25000}.

$$\frac{90000}{121}\left(\frac{3}{25000}+\frac{1}{60^{2}}-0.2\right)$$

Calculate 60 to the power of 2 and get 3600.

$$\frac{90000}{121}\left(\frac{3}{25000}+\frac{1}{3600}-0.2\right)$$

Add \frac{3}{25000} and \frac{1}{3600} to get \frac{179}{450000}.

$$\frac{90000}{121}\left(\frac{179}{450000}-0.2\right)$$

Subtract 0.2 from \frac{179}{450000} to get -\frac{89821}{450000}.

$$\frac{90000}{121}\left(-\frac{89821}{450000}\right)$$

Multiply \frac{90000}{121} and -\frac{89821}{450000} to get -\frac{89821}{605}.

$$-\frac{89821}{605}$$

Factor

$$-\frac{89821}{605} = -148\frac{281}{605} = -148.46446280991736$$