# How to simplify (6.2 times 10^3)(2 times 10^4)  in scientific notation?

Oct 31, 2015

It is $1.24 \times {10}^{8}$
First thing is to multiply the mantisses ($6.2 \times 2$) and the exponents. There you use the property of exponents: ${a}^{b} \cdot {a}^{c} = {a}^{b + c}$.
So first you get: $\left(6.2 \times {10}^{3}\right) \left(2 \times {10}^{4}\right) = 12.4 \times {10}^{7}$
In scientiffic notation the rule is that mantisse has to be between 0 and 10, so you have to move the decimal point one place left increasing the exponent by 1 at the same time. Finally you get the answer: $1.24 \times {10}^{8}$