Question

Which rules of exponents will be used to evaluate this expression? Check all that apply.

StartFraction left-brace (negative 8) Superscript 4 Baseline right-brace Superscript negative 5 Baseline Over (negative 8) Superscript 6 Baseline EndFraction
product of powers
quotient of powers
power of a power
power of a product
negative exponent
zero exponent

Answer 1

B-quotient of powers

C-power of a power

E-negative exponent

Explanation:

Answer 2

• quotient of powers
• power of a power
• negative exponent

Explanation:

Given

• ( -8⁴)⁻⁵ / ( -8⁶)

Evaluating:

• ( -8⁴)⁻⁵ / ( -8⁶) =
• ( -8⁴ˣ⁻⁵) / ( -8⁶) = ⇒ Power of a power (nᵃ)ᵇ = nᵃᵇ
• (-8⁻²⁰)/( -8⁶) =
• 8⁻²⁰⁻⁶ = ⇒ Quotient of powers nᵃ/nᵇ = nᵃ⁻ᵇ
• 8⁻²⁶ =
• 1/8²⁶ ⇒ Negative exponent n⁻ᵃ = 1 / nᵃ

Used rules:

• quotient of powers
• power of a power
• negative exponent