Simplifying Exponents

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

Evaluate: \( \frac{x^{13}}{x^8} \)

Back

\( x^{5} \) (using the Quotient Rule).

Front

What is any number raised to the power of zero?

Back

Any number raised to the power of zero is always 1.

Front

Evaluate: \( (2^8)^2 \)

Back

\( 2^{16} \) (using the Power of a Power Rule).

Front

What is the Power of a Power Rule?

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

Evaluate: \( \frac{(x^3y^2)^3}{x^2y^{10}} \)

Back

\( \frac{x^7}{y^4} \) (using the Quotient Rule and Power of a Power Rule).

Front

What happens when you multiply two powers with the same base?

Back

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

Front

Evaluate: \( x^5 \cdot x^3 \)

Back

\( x^{8} \) (using the Product Rule).

Front

What is the Product Rule for exponents?

Back

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

Front

Evaluate: \( x^0 \)

Back

1 (any non-zero number raised to the power of zero is 1).