Exponents Rules

Front

What is the rule for dividing exponents with the same base?

Back

When dividing exponents with the same base, subtract the exponent in the denominator from the exponent in the numerator: \( \frac{a^m}{a^n} = a^{m-n} \).

Front

How do you multiply exponents with the same base?

Back

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

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

What is the result of 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 rule for negative exponents?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: \( a^{-n} = \frac{1}{a^n} \) (where \( a \neq 0 \)).

Front

What is the value of \( -3^2 \)?

Back

The value of \( -3^2 \) is \( -9 \) because the negative sign is not included in the exponent.

Front

What happens when you multiply a number by 1?

Back

Multiplying any number by 1 leaves the number unchanged: \( a \times 1 = a \).

Front

What is the value of \( (9)^0 \)?

Back

The value of \( (9)^0 \) is 1, as any non-zero number raised to the power of zero equals 1.

Front

How do you simplify \( \frac{a^m}{a^n} \)?

Back

To simplify \( \frac{a^m}{a^n} \), subtract the exponents: \( a^{m-n} \).

Front

What is the result of \( a^m \times b^m \)?

Back

The result of \( a^m \times b^m \) is \( (ab)^m \) due to the property of exponents.