Simplifying Negative Exponents April 20

Front

What is a negative exponent?

Back

A negative exponent indicates that the base should be taken as the reciprocal. For example, x^(-n) = 1/(x^n).

Front

How do you simplify an expression with a negative exponent?

Back

To simplify an expression with a negative exponent, rewrite it as the reciprocal of the base raised to the positive exponent.

Front

Simplify x^(-3).

Back

1/(x^3).

Front

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

Back

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

Front

Simplify 7^(-2).

Back

1/(7^2) or 1/49.

Front

What happens when you raise a negative exponent to a power?

Back

The negative exponent becomes positive when taken as a reciprocal: (x^(-n))^m = 1/(x^(n*m)).

Front

Simplify (x^(-2) * y^(-3)).

Back

1/(x^2 * y^3).

Front

What is the result of 1/(x^(-4))?

Back

x^4.

Front

How do you handle negative exponents in division?

Back

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

Front

Simplify (3^(-1) * 2^(-2)).

Back

1/(3 * 4) or 1/12.