# How do you multiply 3.65×10^23 by 4.12×10^154 by 1.11×10^(−11) and express the answer in scientific notation?

May 22, 2018

$= 1.669218 \times {10}^{167}$

#### Explanation:

Consider the expression:

$3 {x}^{5} \times 4 {x}^{7} \times 8 {x}^{-} 9$

This could be written as: $3 \times 4 \times 8 \times {x}^{5} \times {x}^{7} \times {x}^{-} 9$

Now multiply the numbers and then add the indices of the base $x$

$= 96 {x}^{12}$

We can apply the same method with the calculation given in scientific notation:

(3.65×10^23) xx (4.12×10^154) xx (1.11×10^(−11))

$= \left(3.65 \times 4.12 \times 1.11\right) \times \left({10}^{23} \times {10}^{154} \times {10}^{-} 11\right)$

Multiply the numbers and add the indices of the base $10$

$= 16.69218 \times {10}^{166}$

$= 1.669218 \times {10}^{167}$