Simplify b^8(2b)^4

Problem

b8*(2*b)4

Solution

1. Apply the power of a product rule to the term (2*b)4 by raising both the coefficient and the variable to the power of 4

(2*b)4=2⋅b4

2. Evaluate the numerical power of 2

2=16

3. Substitute the simplified term back into the original expression.

b8⋅16*b4

4. Apply the product rule for exponents by adding the exponents of the terms with the same base b

b8⋅b4=b(8+4)

b(8+4)=b12

5. Combine the results to write the final simplified expression.

16*b12

Final Answer

b8*(2*b)4=16*b12

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