Question

1. which expression is equivalent to $1000 + 3 \cdot 24$a. $10^{3} + 2^{3} \cdot 3^{2}$b. $10^{2} + 2^{3} \cdot 3^{2}$c. $10^{3} + 2^{2} \cdot 3^{3}$d. $10^{2} + 2^{2} \cdot 3^{3}$most common primes: 2, 3, 5, 7, 11

Explanation:

Step1: Rewrite 1000 as power of 10

$1000 = 10^3$

Step2: Factor 24 into prime exponents

$24 = 2^3 \cdot 3^1$, so $3 \cdot 24 = 3 \cdot 2^3 \cdot 3^1 = 2^3 \cdot 3^2$

Step3: Combine rewritten terms

$1000 + 3 \cdot 24 = 10^3 + 2^3 \cdot 3^2$

Answer:

A. $10^3 + 2^3 \cdot 3^2$