Dividing with 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

How do you simplify an expression with a negative exponent?

Back

To simplify an expression with a negative exponent, rewrite the base as a fraction with 1 in the numerator and the base raised to the positive exponent in the denominator. For example, x^(-3) = 1/(x^3).

Front

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

Back

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

Front

How do you handle negative exponents when dividing?

Back

When dividing with negative exponents, convert the negative exponent to a positive one by moving the base to the opposite side of the fraction. For example, x^(-2) / x^3 = 1/(x^2 * x^3) = 1/(x^5).

Front

What is the result of 2^(-3)?

Back

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

Front

What does the expression (x^(-2) * y^(-3)) simplify to?

Back

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

Front

If a^(-m) = 1/(a^m), what is a^(m-n)?

Back

a^(m-n) = a^m / a^n.

Front

What is the simplified form of (3^(-2) / 3^(-5))?

Back

(3^(-2) / 3^(-5)) = 3^(-2 - (-5)) = 3^(3) = 27.

Front

How do you express 5^(-1) in positive exponent form?

Back

5^(-1) = 1/(5^1) = 1/5.

Front

What is the simplified form of (x^3 / x^(-2))?

Back

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