In the equation $\frac{15.5 \times 12}{\sqrt{\left(3+7.5^2\right)}}$, which number is the exponent?
Answer (2)
Identify the equation: ( 3 + 7. 5 2 ) 15.5 × 12 .
Recognize that 7. 5 2 means 7.5 raised to the power of 2.
Conclude that the exponent is 2.
The exponent in the equation is 2 .
Explanation
Identify the Problem We are given the equation ( 3 + 7. 5 2 ) 15.5 × 12 and asked to identify the exponent.
Locate the Exponent Let's break down the equation and look for exponents. The numbers in the equation are 15.5, 12, 3, and 7.5. The expression 7. 5 2 indicates that 7.5 is raised to the power of 2. Therefore, 2 is the exponent.
Final Answer The exponent in the equation ( 3 + 7. 5 2 ) 15.5 × 12 is 2.
Examples
Understanding exponents is crucial in various fields, such as finance and physics. For instance, calculating compound interest involves using exponents to determine the future value of an investment. If you invest 100 a t anann u a l in t eres t r a t eo f 5 A = P(1 + r)^t , w h ere A i s t h e f u t u re v a l u e , P$ is the principal amount ( 100 ) , r i s t h e in t eres t r a t e ( 0.05 ) , an d t$ is the number of years (10). In this case, the exponent 't' plays a vital role in determining the final value of the investment, showcasing the real-world application of exponents.
The exponent in the equation ( 3 + 7. 5 2 ) 15.5 × 12 is 2, as indicated by 7. 5 2 . This means that 7.5 is raised to the power of 2, which is crucial for calculating the square root in the expression.
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