QUESTION 5*Which expression is equivalent toย (๐4๐4๐งโ1)(๐๐5๐ง3)(m 4 q 4 z โ1 )(mq 5 z 3 ), where ๐m, ๐q, and ๐งz are positive?A) ๐4๐20๐งโ3m 4 q 20 z โ3 B) ๐5๐9๐ง2m 5 q 9 z 2 C) ๐6๐8๐งโ1m 6 q 8 z โ1 D) ๐20๐12๐งโ2m 20 q 12 z โ2
Question
QUESTION 5*Which expression is equivalent toย (๐4๐4๐งโ1)(๐๐5๐ง3)(m 4 q 4 z โ1 )(mq 5 z 3 ), where ๐m, ๐q, and ๐งz are positive?A) ๐4๐20๐งโ3m 4 q 20 z โ3 B) ๐5๐9๐ง2m 5 q 9 z 2 C) ๐6๐8๐งโ1m 6 q 8 z โ1 D) ๐20๐12๐งโ2m 20 q 12 z โ2
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) ๐5๐9๐ง2.
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