Solve 60*10^-10*0.24*10^3/1500*(10^8)^3

$$\frac { 60 \times 10 ^ { - 10 } \times 0.24 \times 10 ^ { 3 } } { 1500 \times ( 10 ^ { 8 } ) ^ { 3 } }$$

Evaluate

$$0.00000000000000000000000000000000096$$

Solution Steps

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

$$\frac{60\times 10^{-7}\times 0.24}{1500\times \left(10^{8}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$\frac{60\times 10^{-7}\times 0.24}{1500\times 10^{24}}$$

Cancel out 60 in both numerator and denominator.

$$\frac{0.24\times 10^{-7}}{25\times 10^{24}}$$

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

$$\frac{0.24}{25\times 10^{31}}$$

Calculate 10 to the power of 31 and get 10000000000000000000000000000000.

$$\frac{0.24}{25\times 10000000000000000000000000000000}$$

Multiply 25 and 10000000000000000000000000000000 to get 250000000000000000000000000000000.

$$\frac{0.24}{250000000000000000000000000000000}$$

Expand \frac{0.24}{250000000000000000000000000000000} by multiplying both numerator and the denominator by 100.

$$\frac{24}{25000000000000000000000000000000000}$$

Reduce the fraction \frac{24}{25000000000000000000000000000000000} to lowest terms by extracting and canceling out 8.

$$\frac{3}{3125000000000000000000000000000000}$$

Factor

$$\frac{3}{2 ^ {30} \cdot 5 ^ {35}} = 9.6 \times 10^{-34}$$