Scientific Notation and Exponents

Front

What is scientific notation?

Back

A way to express very large or very small numbers using powers of ten, in the form a x 10^n, where 1 ≤ a < 10 and n is an integer.

Front

How do you add numbers in scientific notation?

Back

Align the exponents. If they are different, convert one number to have the same exponent as the other before adding the coefficients.

Front

What is the exponent rule for multiplying powers with the same base?

Back

Add the exponents: a^m * a^n = a^(m+n).

Front

What is the exponent rule for dividing powers with the same base?

Back

Subtract the exponents: a^m / a^n = a^(m-n).

Front

What does a negative exponent represent?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: a^-n = 1/a^n.

Front

What is the value of 10^0?

Back

10^0 = 1, because any non-zero number raised to the power of zero is 1.

Front

How do you simplify xy^-7?

Back

xy^-7 = x / y^7, using the rule for negative exponents.

Front

What is the value of (2^3) * (2^4)?

Back

2^3 * 2^4 = 2^(3+4) = 2^7.

Front

What is the value of (3^5) / (3^2)?

Back

3^5 / 3^2 = 3^(5-2) = 3^3.

Front

What is the product of 2n^4 and 6n^4?

Back

2n^4 * 6n^4 = 12n^(4+4) = 12n^8.