Question

simplify. express your answer using positive exponents. \\(4j^{0} \cdot 10j^{-1} \cdot 2j^{-1}\\)

Explanation:

Step1: Simplify $j^0$ and constants

Any non-zero number to the 0 power is 1. Multiply the constant coefficients:
$4 \times 10 \times 2 = 80$; $j^0 = 1$

Step2: Combine $j$ terms with exponents

Use exponent rule $j^a \cdot j^b = j^{a+b}$:
$j^{0 + (-1) + (-1)} = j^{-2}$

Step3: Convert to positive exponents

Use rule $j^{-n} = \frac{1}{j^n}$:
$80j^{-2} = \frac{80}{j^2}$

Answer:

$\frac{80}{j^2}$