Math · Numbers, fractions & decimals
Exponents, Roots, and Scientific Notation
Estimated time includes reading and one quiz. Take the time you need.
Start here: key ideas
- An exponent counts repeated factors, not multiplication by the exponent.
- The square-root sign asks for the nonnegative number whose square is the number inside the sign.
- Scientific notation has one nonzero digit before the decimal.
- Positive powers of ten describe large numbers; negative powers describe small decimals.
What you’ll be able to do
- Interpret exponents and roots.
- Write and operate with scientific notation.
- Check magnitude and sign.
Expand powers when unsure, and use place-value size to check scientific notation.
Meaning of powers and roots
In the power 4³, 4 is the base, or repeated factor, and 3 is the exponent, or number of factors. Thus 4³=4×4×4=64, not 4×3. A negative base needs grouping: (−3)²=9, but −3² means −(3²)=−9.
A square root asks for the nonnegative number whose square equals the number inside the square-root sign. Therefore √81=9. Although both 9 and −9 solve x²=81, the radical symbol √81 names only the nonnegative root.
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