Question

simplify. express your answer using positive exponents. \\(\frac{9bcd}{b^{9}c^{4}d^{4}}\\)

Explanation:

Step1: Apply exponent rule for division

For each variable, use the rule $\frac{x^m}{x^n}=x^{m - n}$.
For \(b\): $\frac{b^1}{b^9}=b^{1 - 9}=b^{-8}=\frac{1}{b^8}$
For \(c\): $\frac{c^1}{c^4}=c^{1 - 4}=c^{-3}=\frac{1}{c^3}$
For \(d\): $\frac{d^1}{d^4}=d^{1 - 4}=d^{-3}=\frac{1}{d^3}$
The coefficient 9 remains as is.

Step2: Combine the terms

Multiply the coefficient and the simplified variable terms:
$9\times\frac{1}{b^8}\times\frac{1}{c^3}\times\frac{1}{d^3}=\frac{9}{b^8c^3d^3}$

Answer:

$\frac{9}{b^{8}c^{3}d^{3}}$