Question

simplify. express your answer using positive exponents.
(10c⁸)(10c⁵)

Explanation:

Step1: Multiply the coefficients and the variables separately

First, multiply the coefficients (the numbers in front of the variables) and then multiply the variables with exponents using the product rule of exponents, which states that \(a^m \cdot a^n = a^{m + n}\).

For the coefficients: \(10 \times 10 = 100\)

For the variable \(c\): \(c^8 \cdot c^5 = c^{8 + 5}\) (by the product rule of exponents)

Step2: Simplify the exponents

Calculate \(8 + 5 = 13\), so \(c^8 \cdot c^5 = c^{13}\)

Then combine the coefficient and the variable: \(100 \times c^{13} = 100c^{13}\)

Answer:

\(100c^{13}\)