Question

-5bc³ × 3b²·c⁵

Explanation:

Step1: Identify like terms and coefficients

We have the expression \(-5bc^{3} \times 3b^{2} \cdot c^{5}\). First, multiply the coefficients: \(-5\) and \(3\). Then, for the variables with \(b\) ( \(b\) and \(b^{2}\)) and variables with \(c\) ( \(c^{3}\) and \(c^{5}\)).

Step2: Multiply coefficients

Multiply the numerical coefficients: \(-5\times3=-15\).

Step3: Multiply \(b\) terms

Using the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\), for \(b\) terms: \(b\times b^{2}=b^{1+2}=b^{3}\).

Step4: Multiply \(c\) terms

For \(c\) terms: \(c^{3}\times c^{5}=c^{3 + 5}=c^{8}\).

Step5: Combine all parts

Combine the coefficient, \(b\) term, and \(c\) term: \(-15\times b^{3}\times c^{8}=-15b^{3}c^{8}\).

Answer:

\(-15b^{3}c^{8}\)