Question

Identifying the Rules of Exponents to Evaluate
Which rules of exponents will be used to evaluate the expression. Check all that apply.
Left-brace (7 Superscript 5 Baseline) (7 cubed) right-brace Superscript negative 4
quotient of powers
product of powers
power of a power
power of a product
negative exponent
zero exponent

Answer 1

Answer: product of powers; power of a power; power of a product; negative exponent.

Reason: ((7^5)(7^3))^-4
- Combine 7^5·7^3 using product of powers → 7^(5+3) = 7^8.
- Raise to -4 using power of a power → (7^8)^-4 = 7^(8·-4) = 7^-32.
- Apply negative exponent rule → 7^-32 = 1 / 7^32.

(Alternatively you could apply power of a product first: (7^5)^-4(7^3)^-4 = 7^-20·7^-12 = 7^-32.)
Quotient of powers and zero exponent are not used.