# How do you simplify (5x10^2)(3x10^-3)?

Feb 3, 2015

I assume the x's are meant as multiplication signs?

Step 1:
Multiply the numbers and the 10-powers separately:
$\left(5 \cdot {10}^{2}\right) \left(3 \cdot {10}^{-} 3\right) = \left(5 \cdot 3\right) \left({10}^{2} \cdot {10}^{-} 3\right)$

Step 2:
Multiply the numbers:
$\left(5 \cdot 3\right) \left({10}^{2} \cdot {10}^{-} 3\right) = 15 \cdot \left({10}^{2} \cdot {10}^{-} 3\right)$

Step 3:
Add the powers of the 10's
$15 \cdot \left({10}^{2} \cdot {10}^{-} 3\right) = 15 \cdot \left({10}^{2 + - 3}\right) = 15 \cdot {10}^{-} 1$

Step 4:
Put the negative power under the division line and simplify further:
$15 \cdot {10}^{-} 1 = \frac{15}{10} ^ 1 = \frac{15}{10} = 1.5$
In correct scientific notation this would be $1.5 \cdot {10}^{0}$