factor out the greatest common factor from the expression.
35^8+35^5+28^3
35^8 = 7^8 5^8
35^5 = 7^5 5^5
28^3 = 7^3 4^3
so, the best you can factor out is 7^3 5^5
in fact, you can only factor out 7^3 from all 3 values
To factor out the greatest common factor from the expression 35^8 + 35^5 + 28^3, we need to find the greatest common factor (GCF) of the terms.
Step 1: Determine the factors of each term
35^8 = 35 * 35 * 35 * 35 * 35 * 35 * 35 * 35
35^5 = 35 * 35 * 35 * 35 * 35
28^3 = 28 * 28 * 28
Step 2: Identify the common factors
The common factors among all three terms are 35 and 28.
Step 3: Determine the lowest exponent for each common factor
For 35, the lowest exponent is 5 (from 35^5).
For 28, the lowest exponent is 1 (from 28^1).
Step 4: Write out the factored expression
Now we can factor out the GCF by raising the common factors to their respective lowest exponents:
GCF: 35^5 * 28^1
Factored expression: (35^5 * 28) + (35^5) + (28^1)
= 35^5 * (28 + 1) + 28
So, the factored expression with the greatest common factor factored out is 35^5 * (28 + 1) + 28.