Exponent Rules

Front

What is the power of a power rule in exponents?

Back

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

Front

Simplify \( (x^3)^5 \)

Back

\( x^{15} \)

Front

What is the product of powers rule in exponents?

Back

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

Front

Simplify \( (x^9)^4 \)

Back

\( x^{36} \)

Front

What is the quotient of powers rule in exponents?

Back

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

Front

Simplify \( \frac{3x^7}{x^4} \)

Back

\( 3x^3 \)

Front

What is the power of a product rule in exponents?

Back

When raising a product to a power, apply the exponent to each factor: \( (ab)^n = a^n b^n \)

Front

Simplify \( (2x^2)^3 \)

Back

\( 2^3x^6 \)

Front

What is the zero exponent rule?

Back

Any non-zero base raised to the power of zero equals one: \( a^0 = 1 \) (where \( a \neq 0 \))

Front

What is the negative exponent rule?

Back

A negative exponent indicates the reciprocal: \( a^{-n} = \frac{1}{a^n} \) (where \( a \neq 0 \))