Exponent Rules Review

Front

What is the quotient rule for exponents?

Back

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

Front

How do you express a negative exponent as a positive exponent?

Back

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

Front

What is the power of a power rule for exponents?

Back

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

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

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

Back

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

Front

How do you simplify \( \frac{k^3}{k^7} \)?

Back

Using the quotient rule: \( \frac{k^3}{k^7} = k^{3-7} = k^{-4} = \frac{1}{k^4} \).

Front

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

Back

Using the power of a power rule: \( (x^3)^4 = x^{3 \cdot 4} = x^{12} \).

Front

How do you simplify \( (5x^5)^2 \)?

Back

Using the power of a product rule: \( (5x^5)^2 = 5^2 \cdot (x^5)^2 = 25x^{10} \).

Front

How do you simplify \( \frac{y^{-4}}{x^{-8}} \)?

Back

Using the negative exponent rule: \( \frac{y^{-4}}{x^{-8}} = \frac{1/y^4}{1/x^8} = \frac{x^8}{y^4} \).

Front

What is the value of \( (5^3x^2y^4)^0 \)?

Back

Any expression raised to the power of zero equals 1: \( (5^3x^2y^4)^0 = 1 \).