The exponent on a when [tex]$a^2$[/tex] is multiplied by [tex]$a^5$[/tex] is
Answer (1)
Apply the rule of exponents: a m ⋅ a n = a m + n .
Add the exponents: 2 + 5 = 7 .
Simplify the expression: a 2 ⋅ a 5 = a 7 .
The exponent on a is 7 .
Explanation
Understanding the Problem We are asked to find the exponent on a when a 2 is multiplied by a 5 . This involves using the properties of exponents to simplify the expression.
Applying the Rule of Exponents To solve this, we use the rule for multiplying exponential terms with the same base, which states that a m ⋅ a n = a m + n , where a is the base and m and n are the exponents.
Calculating the Exponent In our case, we have a 2 ⋅ a 5 . Applying the rule, we add the exponents: 2 + 5 = 7 . Therefore, a 2 ⋅ a 5 = a 7 .
Final Answer The exponent on a when a 2 is multiplied by a 5 is 7.
Examples
Understanding exponents is crucial in many areas, such as calculating compound interest. For example, if you invest money that grows at a rate of 5% per year, the amount after 10 years can be calculated using exponents. Similarly, in physics, exponents are used to describe relationships like the inverse square law for gravitational force, where the force decreases with the square of the distance.
