Solve 2.5*367.5/48*11*10^9*frac{25{3}*10^-6}(3*5^2-4*2.5^2)*1000

$$\frac{ 2.5 \times 367.5 }{ 48 \times 11 \times { 10 }^{ 9 } \times \frac{ 25 }{ 3 } \times { 10 }^{ -6 } } (3 \times { 5 }^{ 2 } -4 \times { 2.5 }^{ 2 } ) \times 1000$$

Evaluate

$$\frac{3675}{352}\approx 10.440340909$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and -6 to get 3.

$$\frac{2.5\times 367.5}{48\times 11\times 10^{3}\times \frac{25}{3}}\left(3\times 5^{2}-4\times 2.5^{2}\right)\times 1000$$

Multiply 2.5 and 367.5 to get 918.75.

$$\frac{918.75}{48\times 11\times 10^{3}\times \frac{25}{3}}\left(3\times 5^{2}-4\times 2.5^{2}\right)\times 1000$$

Multiply 48 and 11 to get 528.

$$\frac{918.75}{528\times 10^{3}\times \frac{25}{3}}\left(3\times 5^{2}-4\times 2.5^{2}\right)\times 1000$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{918.75}{528\times 1000\times \frac{25}{3}}\left(3\times 5^{2}-4\times 2.5^{2}\right)\times 1000$$

Multiply 528 and 1000 to get 528000.

$$\frac{918.75}{528000\times \frac{25}{3}}\left(3\times 5^{2}-4\times 2.5^{2}\right)\times 1000$$

Multiply 528000 and \frac{25}{3} to get 4400000.

$$\frac{918.75}{4400000}\left(3\times 5^{2}-4\times 2.5^{2}\right)\times 1000$$

Expand \frac{918.75}{4400000} by multiplying both numerator and the denominator by 100.

$$\frac{91875}{440000000}\left(3\times 5^{2}-4\times 2.5^{2}\right)\times 1000$$

Reduce the fraction \frac{91875}{440000000} to lowest terms by extracting and canceling out 625.

$$\frac{147}{704000}\left(3\times 5^{2}-4\times 2.5^{2}\right)\times 1000$$

Calculate 5 to the power of 2 and get 25.

$$\frac{147}{704000}\left(3\times 25-4\times 2.5^{2}\right)\times 1000$$

Multiply 3 and 25 to get 75.

$$\frac{147}{704000}\left(75-4\times 2.5^{2}\right)\times 1000$$

Calculate 2.5 to the power of 2 and get 6.25.

$$\frac{147}{704000}\left(75-4\times 6.25\right)\times 1000$$

Multiply 4 and 6.25 to get 25.

$$\frac{147}{704000}\left(75-25\right)\times 1000$$

Subtract 25 from 75 to get 50.

$$\frac{147}{704000}\times 50\times 1000$$

Multiply \frac{147}{704000} and 50 to get \frac{147}{14080}.

$$\frac{147}{14080}\times 1000$$

Multiply \frac{147}{14080} and 1000 to get \frac{3675}{352}.

$$\frac{3675}{352}$$

Factor

$$\frac{3 \cdot 5 ^ {2} \cdot 7 ^ {2}}{11 \cdot 2 ^ {5}} = 10\frac{155}{352} = 10.440340909090908$$