Simplify this expression.
[tex]m^{13} \times m^6=[/tex]
A. [tex]m^{19}[/tex]
B. [tex]m^7[/tex]
C. [tex]m^{18}[/tex]
D. [tex]m^8[/tex]
Answer (2)
Use the rule of exponents: a m × a n = a m + n .
Apply the rule to the expression: m 13 × m 6 = m 13 + 6 .
Calculate the exponent: 13 + 6 = 19 .
The simplified expression is m 19 , so the answer is m 19 .
Explanation
Understanding the problem We are asked to simplify the expression m 13 × m 6 . This involves using the properties of exponents to combine the terms.
Applying the exponent rule To simplify the expression, we use the rule that when multiplying exponential terms with the same base, we add the exponents: a m × a n = a m + n .
Calculation Applying this rule to our expression, we have m 13 × m 6 = m 13 + 6 .
Simplifying the exponent Now, we simply add the exponents: 13 + 6 = 19 . Therefore, the simplified expression is m 19 .
Final Answer Comparing our result with the given options, we see that the correct answer is A. m 19 .
Examples
Exponents are used to calculate compound interest. For example, if you invest money in an account that pays compound interest, the amount of money you have after a certain number of years can be calculated using an exponential expression. Understanding how to simplify exponential expressions can help you understand how your investments grow over time. Suppose you invest $1000 in an account that pays 5% interest compounded annually. After 10 years, the amount of money you have is $1000 \times (1 + 0.05)^{10} = $1628.89. This calculation uses the principles of exponents.
To simplify m 13 × m 6 , add the exponents to get m 19 . Thus, the answer is A. m 19 .
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