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QUESTION 5*Which expression is equivalent toย (๐‘š4๐‘ž4๐‘งโˆ’1)(๐‘š๐‘ž5๐‘ง3)(m 4 q 4 z โˆ’1 )(mq 5 z 3 ), where ๐‘šm, ๐‘žq, and ๐‘งz are positive?A) ๐‘š4๐‘ž20๐‘งโˆ’3m 4 q 20 z โˆ’3 B) ๐‘š5๐‘ž9๐‘ง2m 5 q 9 z 2 C) ๐‘š6๐‘ž8๐‘งโˆ’1m 6 q 8 z โˆ’1 D) ๐‘š20๐‘ž12๐‘งโˆ’2m 20 q 12 z โˆ’2

Question

QUESTION 5*Which expression is equivalent toย (๐‘š4๐‘ž4๐‘งโˆ’1)(๐‘š๐‘ž5๐‘ง3)(m 4 q 4 z โˆ’1 )(mq 5 z 3 ), where ๐‘šm, ๐‘žq, and ๐‘งz are positive?A) ๐‘š4๐‘ž20๐‘งโˆ’3m 4 q 20 z โˆ’3 B) ๐‘š5๐‘ž9๐‘ง2m 5 q 9 z 2 C) ๐‘š6๐‘ž8๐‘งโˆ’1m 6 q 8 z โˆ’1 D) ๐‘š20๐‘ž12๐‘งโˆ’2m 20 q 12 z โˆ’2

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Solution

To find the equivalent expression, we need to multiply the given expressions.

Step 1: Multiply the coefficients of the same variables.

For m, we have m^4 in the first expression and m in the second expression. When we multiply these, we add the exponents, so we get m^(4+1) = m^5.

For q, we have q^4 in the first expression and q^5 in the second expression. When we multiply these, we add the exponents, so we get q^(4+5) = q^9.

For z, we have z^-1 in the first expression and z^3 in the second expression. When we multiply these, we add the exponents, so we get z^(-1+3) = z^2.

Step 2: Combine the results from step 1 to get the final expression.

The final expression is m^5q^9z^2.

So, the answer is B) ๐‘š5๐‘ž9๐‘ง2.

This problem has been solved

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