Solve (4(3.1416)^2/6.67*10^-11(5.98*10^24))(384900000)^3

$$( \frac { 4 ( 3.1416 ) ^ { 2 } } { 6.67 \times 10 ^ { - 11 } ( 5.98 \times 10 ^ { 24 } ) } ) ( 384900000 ) ^ { 3 }$$

Evaluate

$$\frac{28139444134343875872}{4985825}\approx 5.643889253 \cdot 10^{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -11 and 24 to get 13.

$$\frac{4\times 3.1416^{2}}{6.67\times 10^{13}\times 5.98}\times 384900000^{3}$$

Calculate 3.1416 to the power of 2 and get 9.86965056.

$$\frac{4\times 9.86965056}{6.67\times 10^{13}\times 5.98}\times 384900000^{3}$$

Multiply 4 and 9.86965056 to get 39.47860224.

$$\frac{39.47860224}{6.67\times 10^{13}\times 5.98}\times 384900000^{3}$$

Calculate 10 to the power of 13 and get 10000000000000.

$$\frac{39.47860224}{6.67\times 10000000000000\times 5.98}\times 384900000^{3}$$

Multiply 6.67 and 10000000000000 to get 66700000000000.

$$\frac{39.47860224}{66700000000000\times 5.98}\times 384900000^{3}$$

Multiply 66700000000000 and 5.98 to get 398866000000000.

$$\frac{39.47860224}{398866000000000}\times 384900000^{3}$$

Expand \frac{39.47860224}{398866000000000} by multiplying both numerator and the denominator by 100000000.

$$\frac{3947860224}{39886600000000000000000}\times 384900000^{3}$$

Reduce the fraction \frac{3947860224}{39886600000000000000000} to lowest terms by extracting and canceling out 256.

$$\frac{15421329}{155807031250000000000}\times 384900000^{3}$$

Calculate 384900000 to the power of 3 and get 57022169049000000000000000.

$$\frac{15421329}{155807031250000000000}\times 57022169049000000000000000$$

Multiply \frac{15421329}{155807031250000000000} and 57022169049000000000000000 to get \frac{28139444134343875872}{4985825}.

$$\frac{28139444134343875872}{4985825}$$

Factor

$$\frac{2 ^ {5} \cdot 3 ^ {5} \cdot 7 ^ {2} \cdot 11 ^ {2} \cdot 17 ^ {2} \cdot 1283 ^ {3}}{13 \cdot 29 \cdot 5 ^ {2} \cdot 23 ^ {2}} = 5643889252900\frac{3734108}{4985825} = 5643889252900.749$$