Exponent Rules

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 simplify \( \frac{x^6}{x^2} \)?

Back

Using the quotient rule, \( \frac{x^6}{x^2} = x^{6-2} = x^4 \).

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

How do you simplify \( \frac{3x^7}{x^4} \)?

Back

Using the quotient rule, \( \frac{3x^7}{x^4} = 3x^{7-4} = 3x^3 \).

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

How do you simplify \( x^2 \cdot x^3 \)?

Back

Using the product rule, \( x^2 \cdot x^3 = x^{2+3} = x^5 \).

Front

What is the power of a product rule for exponents?

Back

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

Front

How do you simplify \( \left(\frac{x^3}{y^4}\right)^5 \)?

Back

Using the power of a quotient rule, \( \left(\frac{x^3}{y^4}\right)^5 = \frac{x^{3 \cdot 5}}{y^{4 \cdot 5}} = \frac{x^{15}}{y^{20}} \).

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

How do you simplify \( \frac{x^4}{3x^4} \)?

Back

Factor out the common term: \( \frac{x^4}{3x^4} = \frac{1}{3} \).