Question

which rules of exponents will be used to evaluate this expression? select three options.

\\\frac{(-8)^4^{-5}}{(-8)^6}\\

fractional exponent
quotient of powers
power of a power
power of a product
negative exponent
zero exponent

Explanation:

Identify the rules needed for the numerator

Using the Exponent Rules knowledge point

$$ [(-8)^4]^{-5} = (-8)^{4 \cdot (-5)} = (-8)^{-20} $$

This step applies the power of a power rule.

Simplify the quotient expression

Using the Exponent Rules knowledge point

$$ \frac{(-8)^{-20}}{(-8)^6} = (-8)^{-20 - 6} = (-8)^{-26} $$

This step applies the quotient of powers rule.

Evaluate the negative exponent

Using the Negative Exponents knowledge point

$$ (-8)^{-26} = \frac{1}{(-8)^{26}} $$

This step applies the negative exponent rule.

Answer:

• fractional exponent
• quotient of powers (Correct answer)
• power of a power (Correct answer)
• power of a product
• negative exponent (Correct answer)
• zero exponent