(12 × 10^5) ÷ (3 × 10^2
To simplify this expression, you can divide the numerical coefficients and subtract the exponents of the powers of 10.
(12 × 10^5) ÷ (3 × 10^2)
= 12 ÷ 3 × (10^5 ÷ 10^2)
= 4 × 10^(5 - 2)
= 4 × 10^3
Therefore, (12 × 10^5) ÷ (3 × 10^2) simplifies to 4 × 10^3.
To solve this problem, we need to use the rules of exponents and perform the multiplication and division separately. Let's break it down step by step:
Step 1: Multiply the numbers in the numerator (12) and the denominator (3):
12 × 3 = 36
Step 2: Multiply the powers of 10 in the numerator (10^5) and the denominator (10^2):
10^5 × 10^2 = 10^(5+2) = 10^7
Step 3: Divide the result of step 1 (36) by the result of step 2 (10^7):
36 ÷ 10^7
Step 4: Simplify the expression by writing the numerator and denominator in scientific notation:
36 ÷ 10^7 = 3.6 × 10^1 ÷ 10^7
Step 5: Apply the rule of subtracting exponents when dividing:
3.6 × 10^(1-7) = 3.6 × 10^(-6)
So, the simplified expression is 3.6 × 10^(-6).