11/15 bellringer

Front

What is the rule for simplifying the expression \( \frac{M^6}{M^2} \)?

Back

Subtract the exponents: \( 6 - 2 = 4 \), so \( M^4 \).

Front

What is the rule for simplifying the expression \( \left(e^5\right)^{4} \)?

Back

Multiply the exponents: \( 5 \times 4 = 20 \), so \( e^{20} \).

Front

How do you simplify the expression \( \frac{w^5 \times w^4}{w^2} \)?

Back

Combine the exponents in the numerator: \( w^{5+4} = w^9 \), then subtract the exponent in the denominator: \( 9 - 2 = 7 \), so the answer is \( w^7 \).

Front

What is the rule for simplifying the expression \( t^7 \times t^4 \)?

Back

Add the exponents: \( 7 + 4 = 11 \), so the result is \( t^{11} \).

Front

What is the general rule for dividing powers with the same base?

Back

Subtract the exponents: \( a^m \div a^n = a^{m-n} \).

Front

What is the general rule for multiplying powers with the same base?

Back

Add the exponents: \( a^m \times a^n = a^{m+n} \).

Front

What is the power of a power rule in exponents?

Back

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

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

What is the negative exponent rule?

Back

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

Front

How do you simplify the expression \( \frac{a^m}{a^n} \) when \( m < n \)?

Back

Subtract the exponents: \( a^{m-n} \) will be a fraction: \( \frac{1}{a^{n-m}} \).