Question

simplify. express your answer using positive exponents.
$8b \cdot 5b^4$

Explanation:

Step1: Multiply the coefficients

Multiply 8 and 5. So, \(8\times5 = 40\).

Step2: Multiply the variables with exponents

Using the rule of exponents \(a^m\cdot a^n=a^{m + n}\), for \(b\) (which is \(b^1\)) and \(b^4\), we have \(b^1\cdot b^4=b^{1 + 4}=b^5\).

Step3: Combine the results

Combine the coefficient and the variable part. So, \(8b\cdot5b^4=40b^5\).

Answer:

\(40b^5\)