Question

Which expression is equivalent to ((r^-7)^6)?

A. (r⁴2)

B. (r¹/42)

C. (-7r⁶)

D. (1/r)

Answer 1

The expression ((r^-7)^6) simplifies to r^-42, which is equivalent to A. r^42, by multiplying the exponents.

Step-by-step explanation:

The expression ((r^-7)^6) can be simplified using the rules of exponents which state that when you raise a power to a power, you multiply the exponents. Therefore, to simplify this expression:

• First, identify the base r and the exponents -7 and 6.
• Next, multiply the exponents: -7 × 6 = -42.
• The expression simplifies to r^-42, which can also be expressed as 1/r^42 because a negative exponent indicates a reciprocal.

Therefore, the correct answer that represents the equivalent expression to ((r^-7)^6) is A. r^42.