Exponents and Scientific Notation

Front

What is an exponent?

Back

An exponent is a number that indicates how many times to multiply the base by itself. For example, in 5², 5 is the base and 2 is the exponent, meaning 5 is multiplied by itself 2 times (5 x 5).

Front

What is the product of 5³ and 5⁴?

Back

5⁷

Front

How do you simplify a negative exponent?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent. For example, 9⁻³ = 1/9³.

Front

What is scientific notation?

Back

Scientific notation is a way of expressing numbers as a product of a number between 1 and 10 and a power of 10. For example, 3000 can be written as 3 x 10³.

Front

How do you multiply numbers in scientific notation?

Back

To multiply numbers in scientific notation, multiply the coefficients and add the exponents. For example, (3 x 10²) x (2 x 10³) = 6 x 10^(2+3) = 6 x 10⁵.

Front

What is the value of 1.111 x 10¹⁵ compared to 9.999 x 10³?

Back

1.111 x 10¹⁵ is greater because it has a larger exponent.

Front

How do you convert a number from standard form to scientific notation?

Back

To convert to scientific notation, move the decimal point in the number until only one non-zero digit remains to the left. Count the number of places moved; this becomes the exponent of 10.

Front

What is the result of 300.5 x (3 x 10⁵)?

Back

9.015 x 10⁷

Front

How do you add numbers in scientific notation?

Back

To add numbers in scientific notation, they must have the same exponent. If they don't, convert one number to have the same exponent as the other before adding.

Front

What is the simplified form of 9⁻³?

Back

1/9³