Solve 6.022*10^23(4.20)^3*10^-24

$$6.022 \times 10 ^ { 23 } ( 4.20 ) ^ { 3 } \times 10 ^ { - 24 }$$

Evaluate

$$44.6157936$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 23 and -24 to get -1.

$$6.022\times 10^{-1}\times 4.2^{3}$$

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

$$6.022\times \frac{1}{10}\times 4.2^{3}$$

Multiply 6.022 and \frac{1}{10} to get \frac{3011}{5000}.

$$\frac{3011}{5000}\times 4.2^{3}$$

Calculate 4.2 to the power of 3 and get 74.088.

$$\frac{3011}{5000}\times 74.088$$

Multiply \frac{3011}{5000} and 74.088 to get \frac{27884871}{625000}.

$$\frac{27884871}{625000}$$

Factor

$$\frac{3011 \cdot 3 ^ {3} \cdot 7 ^ {3}}{2 ^ {3} \cdot 5 ^ {7}} = 44\frac{384871}{625000} = 44.6157936$$