Solve (21/10)^3*(21/10)^7*(27/10)^8-4

$$( \frac { 21 } { 10 } ) ^ { 3 } \cdot ( \frac { 21 } { 10 } ) ^ { 7 } \cdot ( \frac { 27 } { 10 } ) ^ { 8 } - 4$$

Evaluate

$$\frac{4710887053231557295250681}{1000000000000000000}=4710887.053231557$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 7 to get 10.

$$\left(\frac{21}{10}\right)^{10}\times \left(\frac{27}{10}\right)^{8}-4$$

Calculate \frac{21}{10} to the power of 10 and get \frac{16679880978201}{10000000000}.

$$\frac{16679880978201}{10000000000}\times \left(\frac{27}{10}\right)^{8}-4$$

Calculate \frac{27}{10} to the power of 8 and get \frac{282429536481}{100000000}.

$$\frac{16679880978201}{10000000000}\times \frac{282429536481}{100000000}-4$$

Multiply \frac{16679880978201}{10000000000} times \frac{282429536481}{100000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16679880978201\times 282429536481}{10000000000\times 100000000}-4$$

Do the multiplications in the fraction \frac{16679880978201\times 282429536481}{10000000000\times 100000000}.

$$\frac{4710891053231557295250681}{1000000000000000000}-4$$

Convert 4 to fraction \frac{4000000000000000000}{1000000000000000000}.

$$\frac{4710891053231557295250681}{1000000000000000000}-\frac{4000000000000000000}{1000000000000000000}$$

Since \frac{4710891053231557295250681}{1000000000000000000} and \frac{4000000000000000000}{1000000000000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4710891053231557295250681-4000000000000000000}{1000000000000000000}$$

Subtract 4000000000000000000 from 4710891053231557295250681 to get 4710887053231557295250681.

$$\frac{4710887053231557295250681}{1000000000000000000}$$

Factor

$$\frac{11 \cdot 197496247231 \cdot 2168458719541}{2 ^ {18} \cdot 5 ^ {18}} = 4710887\frac{53231557049319420}{1 \times 10^{18}} = 4710887.053231557$$