Laws of Exponents Practice

Front

What is the Quotient Rule for exponents?

Back

When dividing two powers with the same base, subtract the exponents: \( a^m \div a^n = a^{m-n} \).

Front

Evaluate: \( 9^9 \div 9^4 \) using the Quotient Rule.

Back

\( 9^{9-4} = 9^5 \)

Front

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

Back

Any number (except zero) raised to the power of zero is 1.

Front

Simplify: \( (a^4b^{19}c^{21}d^{-14})^0 \)

Back

1 (Any expression raised to the power of zero equals 1.)

Front

What happens when you raise a power to another power?

Back

You multiply the exponents: \( (a^m)^n = a^{m \cdot n} \).

Front

Evaluate: \( (x^2)^3 \)

Back

\( x^{2 \cdot 3} = x^6 \)

Front

What is the Product Rule for exponents?

Back

When multiplying two powers with the same base, add the exponents: \( a^m \cdot a^n = a^{m+n} \).

Front

Evaluate: \( 5^3 \cdot 5^2 \) using the Product Rule.

Back

\( 5^{3+2} = 5^5 \)

Front

What is the definition of a negative exponent?

Back

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

Front

Evaluate: \( 2^{-3} \)

Back

\( \frac{1}{2^3} = \frac{1}{8} \)