Mathematics » Polynomials II » Integer Exponents and Scientific Notation

# Integer Exponents and Scientific Notation Summary

## 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:
1. Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.
2. Count the number of decimal places, $$n$$, that the decimal point was moved.
3. 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 $${10}^{\text{−}n}$$
4. Check.
• To convert scientific notation to decimal form:
1. Determine the exponent, $$n$$, on the factor 10.
2. 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.
3. Check.

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