Simplify b^8(2b)^7

Problem

b8*(2*b)7

Solution

1. Apply the power of a product rule to the term (2*b)7 by raising both the coefficient and the variable to the power of 7

(2*b)7=2⋅b7

2. Calculate the numerical value of 2

2=128

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

b8⋅128⋅b7

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

b8⋅b7=b(8+7)

b(8+7)=b15

5. Combine the results to write the expression in its simplest form.

128*b15

Final Answer

b8*(2*b)7=128*b15

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