When $6 a^2 b^3 \cdot-3 a^5 b^3$ is multiplied, the product of the coefficients is $\square$. The exponent on a when $a^2$ is multiplied by $a^5$ is $\square$.
Answer (2)
When multiplying terms with the same base, add the exponents.
Add the exponents of a : 2 + 5 = 7 .
The exponent on a when a 2 is multiplied by a 5 is 7.
The final answer is 7 .
Explanation
Understanding the Problem We are given the expression 6 a 2 b 3 × − 3 a 5 b 3 . We need to find the exponent on a when a 2 is multiplied by a 5 .
Multiplying exponents When multiplying terms with the same base, we add the exponents. In this case, we have a 2 × a 5 = a 2 + 5 .
Calculating the exponent Now, we simply add the exponents: 2 + 5 = 7 . Therefore, the exponent on a when a 2 is multiplied by a 5 is 7.
Examples
Understanding exponents is crucial in many fields, such as computer science when calculating storage space or in finance when dealing with compound interest. For example, if a bacteria population doubles every hour, the growth can be modeled using exponents. If you start with one bacterium, after 5 hours, you'll have 2 5 = 32 bacteria. This exponential growth highlights the power of exponents in real-world scenarios.
The product of the coefficients when multiplying 6 a 2 b 3 and − 3 a 5 b 3 is -18. The exponent on 'a' when a 2 is multiplied by a 5 is 7.
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