Exponent Rules

Front

What is the rule for simplifying expressions with exponents when dividing like bases?

Back

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

Front

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

Back

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

Front

How do you simplify an expression with a negative exponent?

Back

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

Front

What is the result of multiplying two powers with the same base?

Back

When multiplying 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 division rule for exponents, \( \frac{3x^7}{x^4} = 3x^{7-4} = 3x^3 \).

Front

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

Back

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

Front

What is the simplified form of \( \frac{3a^{-1}c^{-5}}{d^0} \)?

Back

Since \( d^0 = 1 \), the expression simplifies to \( \frac{3}{ac^5} \).

Front

What is the rule for multiplying powers with different bases but the same exponent?

Back

When multiplying powers with different bases but the same exponent, multiply the bases and keep the exponent: \( a^m \cdot b^m = (ab)^m \).

Front

How do you simplify \( 7p^0 \)?

Back

Since \( p^0 = 1 \), the expression simplifies to \( 7 \cdot 1 = 7 \).

Front

What is the simplified form of \( \frac{8}{xy^8} \)?

Back

The expression is already simplified as \( \frac{8}{xy^8} \).