Exponent Review

Front

What is the quotient rule for exponents when dividing like bases?

Back

When dividing like bases, subtract the exponents: \( \frac{a^m}{a^n} = a^{m-n} \).

Front

How do you simplify the expression \( a^m \cdot a^n \)?

Back

When multiplying like bases, add the exponents: \( a^m \cdot a^n = a^{m+n} \).

Front

What is the power of a power rule for exponents?

Back

When raising a power to another power, multiply the exponents: \( (a^m)^n = a^{m \cdot n} \).

Front

How do you simplify the expression \( (xy)^n \)?

Back

Distribute the exponent to both bases: \( (xy)^n = x^n y^n \).

Front

What is the value of \( a^0 \) for any non-zero number \( a \)?

Back

For any non-zero number \( a \), \( a^0 = 1 \).

Front

What happens when you have a negative exponent, such as \( a^{-n} \)?

Back

A negative exponent indicates a reciprocal: \( a^{-n} = \frac{1}{a^n} \).

Front

How do you simplify the expression \( \frac{a^m}{a^n} \) when \( m < n \)?

Back

When \( m < n \), the result is \( \frac{1}{a^{n-m}} \).

Front

What is the product of powers property?

Back

The product of powers property states that when multiplying two powers with the same base, you add the exponents: \( a^m \cdot a^n = a^{m+n} \).

Front

How do you simplify \( (x^3)^2 \)?

Back

Using the power of a power rule, \( (x^3)^2 = x^{3 \cdot 2} = x^6 \).

Front

What is the simplified form of \( \frac{b^5}{b^2} \)?

Back

Using the quotient rule, \( \frac{b^5}{b^2} = b^{5-2} = b^3 \).