Dividing 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 it as a fraction. For example, x^-3 = 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

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

What does a zero exponent mean?

Back

Any non-zero base raised to the power of zero equals one: a^0 = 1.

Front

How do you express a negative exponent as a positive exponent?

Back

To express a negative exponent as a positive exponent, take the reciprocal of the base: a^-n = 1/a^n.

Front

What is the product of two negative bases?

Back

The product of two negative bases is positive: (-a) * (-b) = ab.

Front

How do you simplify (x^3)/(x^-2)?

Back

To simplify (x^3)/(x^-2), subtract the exponents: x^(3 - (-2)) = x^(3 + 2) = x^5.

Front

What is the result of (2^-3) * (2^5)?

Back

Using the rule for multiplying powers, add the exponents: 2^(-3 + 5) = 2^2.

Front

How do you write 1/(a^-4) using positive exponents?

Back

1/(a^-4) = a^4.