Solve 3.14/64(0.3937^4-0.324^4)=

$$\frac { 3.14 } { 64 } ( 0.3937 ^ { 4 } - 0.324 ^ { 4 } ) =$$

Evaluate

$$0.00063805503183846490625$$

Solution Steps

Expand \frac{3.14}{64} by multiplying both numerator and the denominator by 100.

$$\frac{314}{6400}\left(0.3937^{4}-0.324^{4}\right)$$

Reduce the fraction \frac{314}{6400} to lowest terms by extracting and canceling out 2.

$$\frac{157}{3200}\left(0.3937^{4}-0.324^{4}\right)$$

Calculate 0.3937 to the power of 4 and get 0.0240249039000961.

$$\frac{157}{3200}\left(0.0240249039000961-0.324^{4}\right)$$

Calculate 0.324 to the power of 4 and get 0.011019960576.

$$\frac{157}{3200}\left(0.0240249039000961-0.011019960576\right)$$

Subtract 0.011019960576 from 0.0240249039000961 to get 0.0130049433240961.

$$\frac{157}{3200}\times 0.0130049433240961$$

Convert decimal number 0.0130049433240961 to fraction \frac{130049433240961}{10000000000}. Reduce the fraction \frac{130049433240961}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{157}{3200}\times \frac{130049433240961}{10000000000000000}$$

Multiply \frac{157}{3200} times \frac{130049433240961}{10000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{157\times 130049433240961}{3200\times 10000000000000000}$$

Do the multiplications in the fraction \frac{157\times 130049433240961}{3200\times 10000000000000000}.

$$\frac{20417761018830877}{32000000000000000000}$$

Factor

$$\frac{13 \cdot 17 \cdot 37 \cdot 41 \cdot 157 \cdot 7177 \cdot 54049}{2 ^ {23} \cdot 5 ^ {18}} = 0.0006380550318384649$$