Final answer:
Multiplying and dividing large numbers or numbers with negative powers is easier with scientific notation. To multiply, multiply the coefficients and add the exponents. For division, divide the coefficients and subtract the exponents. Negative exponents indicate a reciprocal.
Step-by-step explanation:
When you're working with numbers with large and negative powers, it's generally easier to use scientific notation, which simplifies arithmetic involving such numbers. In scientific notation, numbers are expressed as powers of ten.
To multiply two numbers expressed as powers of ten, you simply multiply the numbers out front and add the exponents. For example, (3 × 10⁵) × (2 × 10⁹) would become 6 × 10¹⁴. If there are no numbers out front, as in 100 × 100,000, you simply add the exponents, for example, 10² × 10⁵ = 10⁷.
And when it comes to dividing numbers in scientific notation, you divide the numbers out front and subtract the exponents. An example would be 10⁶ / 10³ = 10³.
To deal with negative powers, remember that a negative exponent means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side. For example, 10⁻⁵ is the same as 1 / 10⁵.
Learn more about Multiplying and Dividing Large and Negative Powers