What is the simplified form of ? 8×4 8×8 32×4 32×8
What is the simplified form of ? 8×4 8×8 32×4 32×8
The Correct Answer and Explanation is:
ChatGPT said:
Let’s first simplify the expression:
Expression:8×4×8×8×32×432×8\frac{8 \times 4 \times 8 \times 8 \times 32 \times 4}{32 \times 8}32×88×4×8×8×32×4
Note: The original input had unclear spacing. Interpreting it as:
Numerator: 8×4×8×8×32×48 \times 4 \times 8 \times 8 \times 32 \times 48×4×8×8×32×4
Denominator: 32×832 \times 832×8
Step 1: Multiply the numerator and denominator.
Numerator:8×4×8×8×32×48 \times 4 \times 8 \times 8 \times 32 \times 48×4×8×8×32×4
Group the like terms:
- 8×8×8=5128 \times 8 \times 8 = 5128×8×8=512
- 4×4=164 \times 4 = 164×4=16
- 323232
So:512×16×32512 \times 16 \times 32512×16×32
Let’s simplify step by step:
- 512×16=8192512 \times 16 = 8192512×16=8192
- 8192×32=2621448192 \times 32 = 2621448192×32=262144
So, numerator = 262144
Denominator:32×8=25632 \times 8 = 25632×8=256
Now divide:262144256=1024\frac{262144}{256} = 1024256262144=1024
✅ Final Simplified Answer: 1024
💡 Explanation
To simplify the expression 8×4×8×8×32×432×8\frac{8 \times 4 \times 8 \times 8 \times 32 \times 4}{32 \times 8}32×88×4×8×8×32×4, we first interpret and organize it. The numerator contains a product of six numbers, while the denominator includes two. The goal is to reduce the fraction by canceling common factors.
The expression is a fraction, and any factor that appears both in the numerator and denominator can be simplified. This is a key property of fractions: a×ba=b\frac{a \times b}{a} = baa×b=b, assuming a≠0a \neq 0a=0. So, we look for common numbers in the numerator and denominator.
From the numerator, notice that 8 and 32 also appear in the denominator. One 8 in the numerator cancels with one 8 in the denominator. Similarly, one 32 cancels with one 32.
After canceling, the remaining terms in the numerator are:
- Two 8s (since there were three 8s originally)
- Two 4s
- And no more 32 or 8 from the denominator
So, remaining multiplication:8×8×4×4=64×16=10248 \times 8 \times 4 \times 4 = 64 \times 16 = 10248×8×4×4=64×16=1024
Hence, the simplified form of the expression is 1024.
This kind of simplification helps in solving complex arithmetic or algebraic expressions more efficiently. Recognizing and canceling common factors is a fundamental skill in math that improves accuracy and speed.
