# How do you multiply (6.4*10^4)(8.6*10^8)?

Apr 2, 2015

Multiply the numbers and add the $10$powers:

$\left(6.4 \cdot {10}^{4}\right) \left(8.6 \cdot {10}^{8}\right) = \left(6.4 \cdot 8.6\right) \cdot {10}^{4 + 8}$

$= 55 \cdot {10}^{12} = 5.5 \cdot {10}^{13}$

(decimal point one to the left = power up by one)

Apr 2, 2015

The answer is $5.5 \times {10}^{13}$.

First, multiply the coefficients and add the exponents.

$\left(6.4 \times {10}^{4}\right) \left(8.6 \times {10}^{8}\right) = \left(6.4\right) \left(8.6\right) \times {10}^{\left(4 + 8\right)} = 55 \times {10}^{12}$

Second, move the decimal to the left one place and increase the exponent by one so that the answer is in the correct scientific notation format.

$55 \times {10}^{12} = 5.5 \times {10}^{13}$