Solve (2.97)(11.43x10^-5)(2.13x10^3)/(3.44x10^4)(2.55x10^-3)(10.61)

$$\frac{ (2.97)(11.43x { 10 }^{ -5 } )(2.13x { 10 }^{ 3 } ) }{ (3.44x { 10 }^{ 4 } )(2.55x { 10 }^{ -3 } )(10.61) }$$

Evaluate

$$\frac{24102441}{31023640000}\approx 0.000776906$$

Solution Steps

Multiply x and x to get x^{2}.

$$\frac{2.97\times 11.43x^{2}\times 10^{-5}\times 2.13\times 10^{3}}{3.44x\times 10^{4}\times 2.55x\times 10^{-3}\times 10.61}$$

To multiply powers of the same base, add their exponents. Add -5 and 3 to get -2.

$$\frac{2.97\times 11.43x^{2}\times 10^{-2}\times 2.13}{3.44x\times 10^{4}\times 2.55x\times 10^{-3}\times 10.61}$$

Multiply x and x to get x^{2}.

$$\frac{2.97\times 11.43x^{2}\times 10^{-2}\times 2.13}{3.44x^{2}\times 10^{4}\times 2.55\times 10^{-3}\times 10.61}$$

To multiply powers of the same base, add their exponents. Add 4 and -3 to get 1.

$$\frac{2.97\times 11.43x^{2}\times 10^{-2}\times 2.13}{3.44x^{2}\times 10^{1}\times 2.55\times 10.61}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{2.13\times 2.97\times 11.43\times 10^{-2}}{2.55\times 3.44\times 10.61\times 10^{1}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{2.13\times 2.97\times 11.43}{2.55\times 3.44\times 10.61\times 10^{3}}$$

Multiply 2.13 and 2.97 to get 6.3261.

$$\frac{6.3261\times 11.43}{2.55\times 3.44\times 10.61\times 10^{3}}$$

Multiply 6.3261 and 11.43 to get 72.307323.

$$\frac{72.307323}{2.55\times 3.44\times 10.61\times 10^{3}}$$

Multiply 2.55 and 3.44 to get 8.772.

$$\frac{72.307323}{8.772\times 10.61\times 10^{3}}$$

Multiply 8.772 and 10.61 to get 93.07092.

$$\frac{72.307323}{93.07092\times 10^{3}}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{72.307323}{93.07092\times 1000}$$

Multiply 93.07092 and 1000 to get 93070.92.

$$\frac{72.307323}{93070.92}$$

Expand \frac{72.307323}{93070.92} by multiplying both numerator and the denominator by 1000000.

$$\frac{72307323}{93070920000}$$

Reduce the fraction \frac{72307323}{93070920000} to lowest terms by extracting and canceling out 3.

$$\frac{24102441}{31023640000}$$

Factor

$$\frac{11 \cdot 71 \cdot 127 \cdot 3 ^ {5}}{17 \cdot 43 \cdot 1061 \cdot 2 ^ {6} \cdot 5 ^ {4}} = 0.0007769056435672926$$