## Key Concepts

**Property of Negative Exponents**- If \(n\) is a positive integer and \(a\ne 0\), then \(\frac{1}{{a}^{\text{−}n}}={a}^{n}\)

**Quotient to a Negative Exponent**- If \(a,b\) are real numbers, \(b\ne 0\) and \(n\) is an integer , then \({\left(\frac{a}{b}\right)}^{\text{−}n}={\left(\frac{b}{a}\right)}^{n}\)

**To convert a decimal to scientific notation:**- Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.
- Count the number of decimal places, \(n\), that the decimal point was moved.
- Write the number as a product with a power of 10. If the original number is:
- greater than 1, the power of 10 will be \({10}^{n}\)
- between 0 and 1, the power of 10 will be \({10}^{\text{−}n}\)

- Check.

**To convert scientific notation to decimal form:**- Determine the exponent, \(n\), on the factor 10.
- Move the decimal \(n\)places, adding zeros if needed.
- If the exponent is positive, move the decimal point \(n\) places to the right.
- If the exponent is negative, move the decimal point \(|n|\) places to the left.

- Check.