What are the laws of exponents?

• The laws of exponents, or exponent rules, are a set of guidelines that simplify manipulating expressions involving exponents, such as multiplying, dividing, and raising powers to other powers.

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• Understanding exponents (IXL)

• Evaluate powers (IXL)

• Solve equations with variable exponents (IXL)

• Powers with negative bases (IXL)

• Powers with decimal and fractional bases (IXL)

• Understanding negative exponents (IXL)

• Evaluate powers with negative exponents (IXL)

• Evaluate powers with negative or zero exponents (IXL)

• Multiply powers: integer bases (IXL)

• Divide powers: integer bases (IXL)

• Multiply and divide powers: integer bases (IXL)

• Power of a power: integer bases (IXL)

• Evaluate expressions using properties of exponents (IXL)

• Identify equivalent expressions involving exponents 1 (IXL)

• Identify equivalent expressions involving exponents 2 (IXL)

• Multiply powers: variable bases (IXL)

• Divide powers: variable bases (IXL)

• Multiply and divide powers: variable bases (IXL)

• Powers of a power: variables bases (IXL)

What is scientific notation?

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10^8.

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• Convert between standard and scientific notation (IXL)

• Scientific notation on calculators (IXL)

• Compare numbers written in scientific notation (IXL)

How do we multiply and divide numbers in scientific notation?

Here are the steps to multiply two numbers in scientific notation:

1. Multiply the coefficients--round to the number of significant figures in the coefficient with the smallest number of significant figures.

2. Add the exponents.

3. Convert the result to scientific notation.

Here are the steps to divide two numbers in scientific notation:

1. Divide the coefficients--round to the number of significant figures in the coefficient with the smallest number of significant figures.

2. Subtract the exponents.

3. Convert the result to scientific notation.

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• Multiply numbers written in scientific notation (IXL)

• Divide numbers written in scientific notation (IXL)

How do we add and subtract numbers in scientific notation?

1. Determine the number by which to increase the smaller exponent by so it is equal to the larger exponent.

2. Increase the smaller exponent by this number and move the decimal point of the number with the smaller exponent to the left the same number of places. (i.e. divide by the appropriate power of 10.)

3. Add or subtract the new coefficients.

4. If the answer is not in scientific notation (i.e. if the coefficient is not between 1 and 10) convert it to scientific notation.

5. The answer should include coefficient, base, and exponent.

Need some practice?

• Add and subtract numbers written in scientific notation (IXL)