Laws of Exponents

Front

What is the law of exponents for dividing like bases?

Back

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

Front

Simplify: \( m^{12} / m^{3} \)

Back

\( m^{12-3} = m^{9} \)

Front

What happens to the exponent when raising a power to a power?

Back

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

Front

Simplify: \( x \cdot x \cdot x \cdot x \cdot x \cdot x \)

Back

\( x^6 \)

Front

What is the law of exponents for multiplying like bases?

Back

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

Front

Simplify: \( \frac{x^8y^7z^6}{x^5y^4z^3} \)

Back

\( x^{8-5}y^{7-4}z^{6-3} = x^3y^3z^3 \)

Front

What is the value of \( a^{-n} \)?

Back

\( a^{-n} = \frac{1}{a^n} \) for any non-zero \( a \).

Front

Simplify: \( \frac{1}{a^{-5}} \)

Back

\( a^5 \) because \( \frac{1}{a^{-n}} = a^n \).

Front

What is the result of \( a^0 \)?

Back

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

Front

What is the law of exponents for raising a product to a power?

Back

When raising a product to a power, distribute the exponent: \( (ab)^n = a^n b^n \).