Zero and Negative Exponents

Front

What is the value of any non-zero number raised to the power of zero?

Back

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

Front

How do you simplify a negative exponent, such as a^-n?

Back

A negative exponent indicates the reciprocal: a^-n = 1/aⁿ.

Front

What is the result of simplifying 4^-2?

Back

4^-2 simplifies to \frac{1}{16}.

Front

How do you simplify a fraction with a negative exponent in the denominator, such as \frac{1}{x^{-2}}?

Back

\frac{1}{x^{-2}} simplifies to x².

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/aⁿ = a^m-n.

Front

How do you simplify the expression \frac{x^{-2}}{4y^{-5}}?

Back

\frac{x^{-2}}{4y^{-5}} simplifies to \frac{y^5}{4x^2}.

Front

What is the value of (3)^-3?

Back

(3)^-3 simplifies to \frac{1}{27}.

Front

How do you handle a negative exponent in a product, such as 7a^-5b³?

Back

7a^-5b³ simplifies to \frac{7b^3}{a^5}.

Front

What is the general rule for simplifying expressions with negative exponents?

Back

The general rule is to convert negative exponents to positive by taking the reciprocal of the base.

Front

What happens to the exponent when you take the reciprocal of a base with a negative exponent?

Back

The exponent becomes positive: a^-n = 1/aⁿ.