Question

1 - properties of exponents and order of operations
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completely simplify the expression, and write your answer with no negative exponents:
\\(\frac{n^{-3} w^{9} j}{n^{4} w^{-6} j^{5}}\\)
use the symbol ^ to indicate an exponent.
(for example, the expression 3x^2 would be used to indicate \\(3x^2\\), etc.)
remember to leave no negative exponents in your expression.

answer = □ enter an algebraic expression more.. □ preview syntax error

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Explanation:

Step1: Use exponent rules for division (subtract exponents)

For \( n \): \( n^{-3 - 4}=n^{-7}=\frac{1}{n^{7}} \) (but we'll handle negative exponents later by moving terms)
For \( w \): \( w^{9 - (-6)} = w^{9 + 6}=w^{15} \)
For \( j \): \( j^{1 - 5}=j^{-4}=\frac{1}{j^{4}} \) (again, handle negative exponents)

Step2: Combine and eliminate negative exponents

Rewrite the expression by moving terms with negative exponents to the denominator or numerator:
\( \frac{n^{-3}w^{9}j}{n^{4}w^{-6}j^{5}}=\frac{w^{9} \cdot w^{6}}{n^{4} \cdot n^{3} \cdot j^{5} \cdot j^{-1}} \) (moved \( n^{-3} \) to denominator as \( n^{3} \), \( w^{-6} \) to numerator as \( w^{6} \), \( j \) to numerator as \( j^{1} \), \( j^{5} \) to denominator)
Simplify exponents:
For \( n \): \( n^{4 + 3}=n^{7} \)
For \( w \): \( w^{9 + 6}=w^{15} \)
For \( j \): \( j^{5 - 1}=j^{4} \)
So the expression becomes \( \frac{w^{15}}{n^{7}j^{4}} \)

Answer:

\( \frac{w^{15}}{n^{7}j^{4}} \) (or in the required format with ^: \( w^15/(n^7j^4) \))