Negative Exponents

Front

What is a negative exponent?

Back

A negative exponent indicates that the base should be taken as the reciprocal and raised to the opposite positive exponent. For example, a^(-n) = 1/(a^n).

Front

Simplify: 2^(-3)

Back

1/(2^3) = 1/8.

Front

What happens when any number is raised to the power of zero?

Back

Any non-zero number raised to the power of zero equals 1.

Front

Simplify: x^(-2)

Back

1/(x^2).

Front

What is the rule for multiplying exponents with the same base?

Back

When multiplying exponents with the same base, add the exponents: a^m * a^n = a^(m+n).

Front

What is the rule for dividing exponents with the same base?

Back

When dividing exponents with the same base, subtract the exponents: a^m / a^n = a^(m-n).

Front

Simplify: 5^0

Back

1.

Front

If a^(-m) = 1/(a^m), what is the value of 3^(-2)?

Back

1/(3^2) = 1/9.

Front

What mistake did a student make if they wrote a^(-2) as a^2?

Back

The student incorrectly interpreted the negative exponent as a positive exponent.

Front

What is the equivalent of 10^(-1)?

Back

1/(10^1) = 1/10.