Which is equal to $2.6 \times 2.6 \times 2.6 \times 2.6$?
A. $(2.6)^4$
B. $4 \times 2.6$
C. $26^2$
D. $4^{2.6}$
Answer (2)
Recognize that 2.6 × 2.6 × 2.6 × 2.6 is equivalent to ( 2.6 ) 4 .
Evaluate the expression ( 2.6 ) 4 .
Compare the result with the given options.
The correct answer is ( 2.6 ) 4 .
Explanation
Understanding the Problem Let's analyze the problem. We are given the expression 2.6 × 2.6 × 2.6 × 2.6 and we need to find which of the given options is equal to it. The options are ( 2.6 ) 4 , 4 × 2.6 , 2 6 2 , and 4 2.6 .
Simplifying the Expression The expression 2.6 × 2.6 × 2.6 × 2.6 can be written as ( 2.6 ) 4 . Let's calculate the value of ( 2.6 ) 4 .
Evaluating the Options Now, let's evaluate the given options:
Option 1: ( 2.6 ) 4 This is the same as 2.6 × 2.6 × 2.6 × 2.6 , so it is equal to the given expression.
Option 2: 4 × 2.6 4 × 2.6 = 10.4
Option 3: 2 6 2 2 6 2 = 26 × 26 = 676
Option 4: 4 2.6 This is equal to 4 2.6 ≈ 36.76
Finding the Correct Option Comparing the values, we see that ( 2.6 ) 4 is equal to 2.6 × 2.6 × 2.6 × 2.6 .
Final Answer Therefore, the expression equal to 2.6 × 2.6 × 2.6 × 2.6 is ( 2.6 ) 4 .
Examples
Exponents are useful in many real-world situations. For example, calculating compound interest involves raising a number to a power. If you invest money at an interest rate, the amount you have after a certain number of years can be calculated using exponents. Also, exponents are used in scientific notation to represent very large or very small numbers, such as the distance to stars or the size of atoms. Understanding exponents helps in these calculations and provides a way to express repeated multiplication concisely.
The expression equal to 2.6 × 2.6 × 2.6 × 2.6 is ( 2.6 ) 4 . Therefore, the correct answer is option A: ( 2.6 ) 4 .
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