Front

What is the Quotient Rule for exponents?

Back

The Quotient Rule states that when dividing two powers with the same base, you subtract the exponents: \( \frac{a^m}{a^n} = a^{m-n} \).

Front

What is the Power of a Power Rule for exponents?

Back

The Power of a Power Rule states that when raising a power to another power, you multiply the exponents: \( (a^m)^n = a^{m \cdot n} \).

Front

What is the Power of a Product Rule for exponents?

Back

The Power of a Product Rule states that when raising a product to a power, you distribute the exponent to each factor: \( (ab)^n = a^n b^n \).

Front

What is the Power of a Quotient Rule for exponents?

Back

The Power of a Quotient Rule states that when raising a quotient to a power, you distribute the exponent to the numerator and denominator: \( \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} \).

Front

What is the value of any non-zero number raised to the power of 0?

Back

Any non-zero number raised to the power of 0 is equal to 1: \( a^0 = 1 \) (where \( a \neq 0 \)).

Front

What is the value of 7 raised to the power of 0?

Back

7 raised to the power of 0 is equal to 1: \( 7^0 = 1 \).

Front

What is the result of squaring a negative number?

Back

Squaring a negative number results in a positive number: \( (-a)^2 = a^2 \).

Front

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

Back

Using the Quotient Rule, you subtract the exponents: \( \frac{x^3}{x^2} = x^{3-2} = x^1 = x \).

Front

What is the simplified form of \( (x^3)^4 \)?

Back

Using the Power of a Power Rule, you multiply the exponents: \( (x^3)^4 = x^{3 \cdot 4} = x^{12} \).

Front

How do you express \( \frac{k^3}{k^7} \) with a positive exponent?

Back

Using the Quotient Rule, you subtract the exponents: \( \frac{k^3}{k^7} = k^{3-7} = k^{-4} \). To express it with a positive exponent, write it as \( \frac{1}{k^4} \).