Rewrite the product as an exponent: [tex]y^4 y^9[/tex]
Answer (2)
Use the property of exponents: a m a n = a m + n .
Apply the property to the given expression: y 4 y 9 = y 4 + 9 .
Calculate the sum of the exponents: 4 + 9 = 13 .
Write the final expression: y 13 . The answer is y 13 .
Explanation
Understanding the problem We are asked to rewrite the product y 4 y 9 as a single exponent. This involves using the properties of exponents to simplify the expression.
Applying the exponent rule To rewrite the product of exponents with the same base, we use the rule: a m a n = a m + n , where a is the base and m and n are the exponents. In our case, the base is y , and the exponents are 4 and 9.
Adding the exponents Applying the rule, we have: y 4 y 9 = y 4 + 9 Now, we need to add the exponents: 4 + 9 = 13 .
Final expression Therefore, the simplified expression is y 13 .
Examples
Exponents are used in various fields, such as calculating compound interest, where the amount increases exponentially over time. For example, if you invest money in a bank account with compound interest, the formula to calculate the future value is A = P ( 1 + r / n ) n t , where A is the future value, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. Understanding exponents helps in predicting the growth of investments or populations over time.
We can rewrite the product y 4 y 9 as a single exponent by applying the exponent rule which states that when multiplying like bases we add their exponents. This gives us y 4 + 9 = y 13 . Therefore, the final answer is (y^{13}.
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