Question

For all integer values of x, which of the following is equal to ((7m³)m⁴)³?

(A) 7m³
(B) 7m¹⁰
(C) 343m²¹
(D) 2401m³
(E) 2401m²¹

Answer 1

When exponentiating the expression ((7m³)m⁴)³, the powers of m are added together inside the parentheses and then that result is raised to the third power, yielding 343m²¹. Therefore, the correct answer is (C) 343m²¹.

Step-by-step explanation:

The question requires simplifying the expression ((7m³)m⁴)³. To do this, we use the rules of exponents, where powers are multiplied when one exponent is raised to another. First, we simplify the inside expression by multiplying the exponents of m:

• 7m³ × m⁴ = 7m(3+4) = 7m·

After simplifying the inside, we raise that expression to the power of 3:

• (7m·)3 = 73m(7×3) = 343m21

So, the correct answer is 343m²¹, which corresponds to choice (C).