Let's solve the expression step-by-step:
Given expression:
[tex]\[ \frac{6^2 \times 7^3 \times 2^3}{4^6 \times 5} \][/tex]
1. Calculate the components in the numerator:
- [tex]\( 6^2 = 36 \)[/tex]
- [tex]\( 7^3 = 343 \)[/tex]
- [tex]\( 2^3 = 8 \)[/tex]
Now multiply these values together:
[tex]\[ 36 \times 343 \times 8 \][/tex]
First, multiply [tex]\( 36 \times 343 \)[/tex]:
[tex]\[ 36 \times 343 = 12348 \][/tex]
Then multiply the result by [tex]\( 8 \)[/tex]:
[tex]\[ 12348 \times 8 = 98784 \][/tex]
So, the numerator is [tex]\( 98784 \)[/tex].
2. Calculate the components in the denominator:
- [tex]\( 4^6 = 4096 \)[/tex]
- There is also a multiplication by [tex]\( 5 \)[/tex]
Now, multiply [tex]\( 4096 \times 5 \)[/tex]:
[tex]\[ 4096 \times 5 = 20480 \][/tex]
So, the denominator is [tex]\( 20480 \)[/tex].
3. Now, divide the numerator by the denominator:
[tex]\[ \frac{98784}{20480} \][/tex]
Performing the division:
[tex]\[ \frac{98784}{20480} = 4.8234375 \][/tex]
Hence, the expression simplifies to:
[tex]\[ \frac{6^2 \times 7^3 \times 2^3}{4^6 \times 5} = 4.8234375 \][/tex]
To summarize, the values are:
- Numerator: [tex]\( 98784 \)[/tex]
- Denominator: [tex]\( 20480 \)[/tex]
- Result: [tex]\( 4.8234375 \)[/tex]
