Identify the base and the exponent in the expression \((-2)^5\). Here, the base is \(-2\) and the exponent is \(5\).
Understand that the exponent \(5\) indicates that the base \(-2\) should be multiplied by itself a total of 5 times.
Write out the multiplication: \((-2) \times (-2) \times (-2) \times (-2) \times (-2)\).
Calculate the product step by step, starting with the first two numbers: \((-2) \times (-2) = 4\).
Continue multiplying the result by the next \(-2\) until all factors are used: \(4 \times (-2)\), then \(-8 \times (-2)\), and so on.
Recommended similar problem, with video answer:
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1m
Play a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Exponents
Exponents represent the number of times a base is multiplied by itself. In the expression (-2)^5, the base is -2, and the exponent is 5, indicating that -2 should be multiplied by itself five times. Understanding how to apply exponents is crucial for evaluating expressions involving powers.
Negative numbers are values less than zero, and they can affect the outcome of mathematical operations, especially when raised to an exponent. In this case, raising a negative number to an odd exponent results in a negative product, which is essential to remember when evaluating expressions like (-2)^5.
The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. When evaluating expressions, it is important to follow these rules, particularly when dealing with exponents, multiplication, and addition, to arrive at the correct answer.