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

Explanation:

Step1: Combine exponents inside parentheses

When multiplying terms with the same base, add exponents: $(7m^3)m^4 = 7m^{3+4} = 7m^7$

Step2: Apply outer exponent to each term

Raise the coefficient and the variable to the 3rd power: $(7m^7)^3 = 7^3 \cdot (m^7)^3$

Step3: Calculate coefficient and variable exponent

$7^3 = 343$, and for the variable, multiply exponents: $(m^7)^3 = m^{7 \times 3} = m^{21}$
Combine results: $343m^{21}$

Answer:

(C) $343m^{21}$