Solve pi/4*{left(7272*2.72*10^5/1125right)}^2*left(10*10^-2right)^2/0.3*1500*800

$$\frac{ \pi }{ 4 } \times { \left( \frac{ 7272 \times 2.72 \times { 10 }^{ 5 } }{ 1125 } \right) }^{ 2 } \times \frac{ { \left(10 \times { 10 }^{ -2 } \right) }^{ 2 } }{ 0.3 \cdot 1500 \cdot 800 }$$

Evaluate

$$\frac{3018843136\pi }{140625}\approx 67441.602975272$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and -2 to get -1.

$$\frac{\pi }{4}\times \left(\frac{7272\times 2.72\times 10^{5}}{1125}\right)^{2}\times \frac{\left(10^{-1}\right)^{2}}{0.3\times 1500\times 800}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$\frac{\pi }{4}\times \left(\frac{7272\times 2.72\times 10^{5}}{1125}\right)^{2}\times \frac{10^{-2}}{0.3\times 1500\times 800}$$

Multiply 7272 and 2.72 to get 19779.84.

$$\frac{\pi }{4}\times \left(\frac{19779.84\times 10^{5}}{1125}\right)^{2}\times \frac{10^{-2}}{0.3\times 1500\times 800}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{\pi }{4}\times \left(\frac{19779.84\times 100000}{1125}\right)^{2}\times \frac{10^{-2}}{0.3\times 1500\times 800}$$

Multiply 19779.84 and 100000 to get 1977984000.

$$\frac{\pi }{4}\times \left(\frac{1977984000}{1125}\right)^{2}\times \frac{10^{-2}}{0.3\times 1500\times 800}$$

Divide 1977984000 by 1125 to get 1758208.

$$\frac{\pi }{4}\times 1758208^{2}\times \frac{10^{-2}}{0.3\times 1500\times 800}$$

Calculate 1758208 to the power of 2 and get 3091295371264.

$$\frac{\pi }{4}\times 3091295371264\times \frac{10^{-2}}{0.3\times 1500\times 800}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{\pi }{4}\times 3091295371264\times \frac{\frac{1}{100}}{0.3\times 1500\times 800}$$

Multiply 0.3 and 1500 to get 450.

$$\frac{\pi }{4}\times 3091295371264\times \frac{\frac{1}{100}}{450\times 800}$$

Multiply 450 and 800 to get 360000.

$$\frac{\pi }{4}\times 3091295371264\times \frac{\frac{1}{100}}{360000}$$

Express \frac{\frac{1}{100}}{360000} as a single fraction.

$$\frac{\pi }{4}\times 3091295371264\times \frac{1}{100\times 360000}$$

Multiply 100 and 360000 to get 36000000.

$$\frac{\pi }{4}\times 3091295371264\times \frac{1}{36000000}$$

Multiply 3091295371264 and \frac{1}{36000000} to get \frac{12075372544}{140625}.

$$\frac{\pi }{4}\times \frac{12075372544}{140625}$$

Multiply \frac{\pi }{4} times \frac{12075372544}{140625} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\pi \times 12075372544}{4\times 140625}$$

Cancel out 4 in both numerator and denominator.

$$\frac{3018843136\pi }{140625}$$

Expand

$$\frac{3018843136 \pi}{140625} = 67441.60297527163$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and -2 to get -1.

$$\frac{\pi }{4}\times \left(\frac{7272\times 2.72\times 10^{5}}{1125}\right)^{2}\times \frac{\left(10^{-1}\right)^{2}}{0.3\times 1500\times 800}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$\frac{\pi }{4}\times \left(\frac{7272\times 2.72\times 10^{5}}{1125}\right)^{2}\times \frac{10^{-2}}{0.3\times 1500\times 800}$$

Multiply 7272 and 2.72 to get 19779.84.

$$\frac{\pi }{4}\times \left(\frac{19779.84\times 10^{5}}{1125}\right)^{2}\times \frac{10^{-2}}{0.3\times 1500\times 800}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{\pi }{4}\times \left(\frac{19779.84\times 100000}{1125}\right)^{2}\times \frac{10^{-2}}{0.3\times 1500\times 800}$$

Multiply 19779.84 and 100000 to get 1977984000.

$$\frac{\pi }{4}\times \left(\frac{1977984000}{1125}\right)^{2}\times \frac{10^{-2}}{0.3\times 1500\times 800}$$

Divide 1977984000 by 1125 to get 1758208.

$$\frac{\pi }{4}\times 1758208^{2}\times \frac{10^{-2}}{0.3\times 1500\times 800}$$

Calculate 1758208 to the power of 2 and get 3091295371264.

$$\frac{\pi }{4}\times 3091295371264\times \frac{10^{-2}}{0.3\times 1500\times 800}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{\pi }{4}\times 3091295371264\times \frac{\frac{1}{100}}{0.3\times 1500\times 800}$$

Multiply 0.3 and 1500 to get 450.

$$\frac{\pi }{4}\times 3091295371264\times \frac{\frac{1}{100}}{450\times 800}$$

Multiply 450 and 800 to get 360000.

$$\frac{\pi }{4}\times 3091295371264\times \frac{\frac{1}{100}}{360000}$$

Express \frac{\frac{1}{100}}{360000} as a single fraction.

$$\frac{\pi }{4}\times 3091295371264\times \frac{1}{100\times 360000}$$

Multiply 100 and 360000 to get 36000000.

$$\frac{\pi }{4}\times 3091295371264\times \frac{1}{36000000}$$

Multiply 3091295371264 and \frac{1}{36000000} to get \frac{12075372544}{140625}.

$$\frac{\pi }{4}\times \frac{12075372544}{140625}$$

Multiply \frac{\pi }{4} times \frac{12075372544}{140625} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\pi \times 12075372544}{4\times 140625}$$

Cancel out 4 in both numerator and denominator.

$$\frac{3018843136\pi }{140625}$$