Question

Please Simplify: (6)3(-2)3 ______ (3)2(2)3
a) -32
b) -24
c) -16
d) 12

Answer 1

The expression (6)^3(-2)^3 over (3)^2(2)^3 simplifies to -24. You calculate the numerator and denominator separately before dividing them to get the final answer.

Step-by-step explanation:

We are asked to simplify the expression (6)3(-2)3 over (3)2(2)3. Let's simplify the expression step by step:

• First, we calculate the numerator (6)3(-2)3. Since both numbers are being raised to the power of 3, we can calculate them separately:
  (6)3 = 6 × 6 × 6 = 216
  (-2)3 = -2 × -2 × -2 = -8
• The product of 216 and -8 is -1728.
• Now, we simplify the denominator (3)2(2)3:
  (3)2 = 3 × 3 = 9
  (2)3 = 2 × 2 × 2 = 8
• The product of 9 and 8 is 72.
• Finally, we divide the numerator by the denominator:
  -1728 ÷ 72 = -24.

Therefore, the simplified form of the expression is -24, which corresponds to option b).