Complete the following exercise:
664⋅4316=
To solve this problem, we'll follow these steps:
- Step 1: Simplify 64.
- Step 2: Simplify with 6.
- Step 3: Simplify 316.
- Step 4: Simplify with 4.
- Step 5: Combine the simplified results.
Now, let's work through each step:
Step 1: Simplify 64.
Since 64=82, we have 64=8.
Step 2: Simplify 68 using exponent rules:
68=81/6.
Step 3: Simplify 316.
Since 16=24, then 316=(24)1/3=24/3.
Step 4: Simplify 424/3 using exponent rules:
We have 424/3=(24/3)1/4=24/12=21/3.
Step 5: Combine simplified results:
We have 81/6⋅21/3=(23)1/6⋅21/3=23/6⋅21/3=21/2⋅21/3=2(1/2+1/3)=2(3/6+2/6)=25/6.
Convert to a common root form:
The result is equivalent to 25/6=12210=121024.
Therefore, the solution to the problem is 121024.
121024