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Writing and Evaluating Expressions with Exponents

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Basics on the topic Writing and Evaluating Expressions with Exponents

Writing and Evaluating Expressions with Exponents

Exponents are a critical component of algebra and are essential for simplifying and solving mathematical expressions efficiently. They provide a shorthand way of expressing repeated multiplication and significantly streamline the representation and calculation of large numbers. By understanding exponents, students can unlock new levels of mathematical proficiency and tackle more complex problems with confidence.

An exponent is a small numeral, known as the power, placed to the upper right of a base number, indicating how many times the base number is to be multiplied by itself. The expression 525^{2}, for instance, means that the base, 55, is used twice in multiplication: 5×55 \times 5.

Writing Expressions with Exponents – Explanation

When it comes to writing expressions using exponential notation, it's crucial to understand the basic rules and how they can be applied to represent multiplication and division succinctly. Expressions with exponents can include positive powers, negative powers, and even powers of powers.

Evaluating Expressions with Exponents – Example

Evaluating expressions with exponents requires careful adherence to the order of operations. By following theorder of operations, you ensure accurate calculations. Let's evaluate the expression 23×(2+3)2^{3} \times (2 + 3). First, calculate the exponent: 23=82^{3} = 8. Then add the numbers inside the parentheses: 2+3=52 + 3 = 5. Finally, multiply the results: 8×5=408 \times 5 = 40.

Writing Expressions with Exponents – Application

Writing Expressions with Exponents – Summary

Key Learnings from this Text:

  • Exponents simplify the representation of repeated multiplication.
  • Positive exponents indicate the number of times a base is multiplied by itself.
  • Negative exponents represent division or taking the reciprocal of the base.
  • Writing and evaluating expressions correctly involves following the rules of exponents and order of operations.

Continue practicing writing and evaluating expressions with exponents to solidify your understanding of this fundamental math concept.

Writing Expressions with Exponents – Frequently Asked Questions

Transcript Writing and Evaluating Expressions with Exponents

Ever since she was a little girl, Leelee's wanted to be famous, but now that she’s a teenager, she realizes that she’s not especially good at anything. Poor Leelee, she realizes she may have an impossible dream, but one day, by complete accident, she made the most amazing video. Really, it's amazing! Leelee thinks that this video is her ticket to stardom and wonders, how long will it take until the video will go viral? Let’s help Leelee figure it out by using expressions with exponents. Leelee has a plan, as soon as her amazing video uploads, she'll send it to three friends and ask each friend to send it to three friends, and then ask each of those friends to send it to three of their friends, and so on, and so on. The video is really short, so Leelee figures that it should only take a minute for each of her three friends to watch the amazing video and then share it with three of their friends, and so on, and so on. Let’s write this information in a chart. After the first minute, her three friends will have watched the video, so that makes three views. After they each share it with three friends, that'll be another nine views. And, when those friends each share it with three more, that'll be another 27 views. Oh boy! By minute four, those 27 friends will each share with three of their friends, so that’s another 81 more views. Do you see a pattern? The number of views grows exponentially, so we can write each of these expressions using a base and an exponent. Let's take a look: 3 is equal to 31. 3 times 3 is the same as 3 squared, which we all know is 9, and 3 times 3 times 3 is equal to 3 cubed or 27, and so on, and so on. For each of these exponent expressions, the base, the number we multiply, remains the same. But the exponent, the number of times we multiply the base with itself, increases by one each time. What’s really neat is you can use this pattern to write an expression to calculate how many new views there will be any given minute. We can write this as 3 raised to the 'x' power, with ‘x’ representing the given minute. Leelee is impatient. She wants to be super famous ASAP. But what if she shares the video with five people, and they each share it with five people, and so on, and so on. At minute 10, how many new views will there be? If we multiply 5 by itself 10 times, that's the same as 5 raised to the 10th power! Calculating this out, there will be 9,765,625 people watching her video at minute 10. WOW! Leelee is really psyched! The video has finally finished uploading! She's gonna watch it so that she can be the very first viewer of this soon-to-be-famous video. Soooo cool! Just like Leelee predicted, the video went viral, and the fly is really famous, but Leelee - not so much.

Writing and Evaluating Expressions with Exponents exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Writing and Evaluating Expressions with Exponents.