Simplify: [tex]\left(-3 j^7 k^5\right)\left(-8 j k^8\right)[/tex]
Answer (2)
Multiply the coefficients: − 3 × − 8 = 24 .
Multiply the j terms: j 7 × j = j 7 + 1 = j 8 .
Multiply the k terms: k 5 × k 8 = k 5 + 8 = k 13 .
Combine the results: The simplified expression is 24 j 8 k 13 .
Explanation
Understanding the Problem We are given the expression ( − 3 j 7 k 5 ) ( − 8 j k 8 ) to simplify. Our goal is to combine like terms and simplify the expression into the form C j m k n , where C is a constant and m and n are integers.
Multiplying Coefficients First, let's multiply the coefficients: − 3 × − 8 = 24 . A negative times a negative gives a positive.
Multiplying j Terms Next, let's multiply the j terms: j 7 × j . Remember that j is the same as j 1 . Using the rule x a × x b = x a + b , we have j 7 × j 1 = j 7 + 1 = j 8 .
Multiplying k Terms Now, let's multiply the k terms: k 5 × k 8 . Using the same rule x a × x b = x a + b , we have k 5 × k 8 = k 5 + 8 = k 13 .
Combining the Results Finally, let's combine all the results: 24 × j 8 × k 13 = 24 j 8 k 13 . So, the simplified expression is 24 j 8 k 13 .
Final Answer The simplified expression is 24 j 8 k 13 . Therefore, the answer is 24 j 8 k 13 .
Examples
Understanding how to simplify expressions with exponents is crucial in many fields, such as physics and engineering. For example, when calculating the energy of a photon, E = h f , where f is the frequency, which can be related to wavelength λ by f = c / λ . If you have multiple photons, you might need to simplify expressions involving powers of these variables to determine total energy or intensity. Simplifying such expressions allows for easier calculations and a better understanding of the relationships between different physical quantities.
To simplify the expression ( − 3 j 7 k 5 ) ( − 8 j k 8 ) , we first multiply the coefficients and variables separately. The result is 24 j 8 k 13 .
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