Question

express the following fraction in simplest form, only using positive exponents.\\(\frac{-10j^8}{-2(j)^4}\\)

Explanation:

Step1: Simplify the coefficients

The coefficients are \(-10\) and \(-2\). Divide \(-10\) by \(-2\): \(\frac{-10}{-2} = 5\).

Step2: Simplify the variable terms

For the variable \(j\), we use the quotient rule of exponents \( \frac{a^m}{a^n}=a^{m - n}\). Here, \(m = 8\) and \(n = 4\), so \(\frac{j^8}{j^4}=j^{8 - 4}=j^4\).

Step3: Combine the results

Multiply the simplified coefficient and the simplified variable term: \(5\times j^4 = 5j^4\).

Answer:

\(5j^4\)