Core 8: Properties of Exponents

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 \( \frac{8^7}{8^2} \)?

Back

Using the quotient rule: \( 8^{7-2} = 8^5 \).

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 \( (xy)^6 \)?

Back

Using the power of a product rule: \( (xy)^6 = x^6y^6 \).

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 \( \frac{x^7}{x^2} \)?

Back

Using the quotient rule: \( x^{7-2} = x^5 \).

Front

What is the product of powers rule?

Back

When multiplying powers with the same base, add the exponents: \( m \cdot m^5 \, \cdot m^6 = m^{1+5+6} = m^{12} \).

Front

What is the base in the expression \( y^5 \)?

Back

The base is \( y \).

Front

What does an exponent of 1 indicate?

Back

An exponent of 1 indicates that the base is used once: \( a^1 = a \).

Front

How do you express \( m \cdot m^5 \cdot m^6 \) using exponents?

Back

Combine the exponents: \( m^{1+5+6} = m^{12} \).