Simplifying an exponential expression | Algebra II | Khan Academy

TL;DR

Learn how to simplify complex exponential expressions by applying exponent properties and breaking down the components.

Transcript

• [Voiceover] What I hope to do in this video is get some practice simplifying some fairly hairy exponential expressions. So let's get started. Let's say that I have the expression 10 times nine to the t over two plus two power, times five to the three t. And what I wanna do is simplify this as much as possible, and preferably get it in the form of... Read More

Key Insights

• ✊ Exponent properties, such as the product of powers and power of a power, can be used to simplify complex exponential expressions.
• 😑 Breaking down the components of the expression and rearranging them can help in simplification.
• ✊ Obtaining as many terms raised to the power of t as possible allows for further simplification.

Questions & Answers

Q: How can the expression 10 times nine to the t over two plus two power, times five to the three t be simplified?

The expression can be simplified by breaking it down using exponent properties. By rewriting each term according to the properties, we can obtain a simpler form. For example, nine to the t over two plus two can be written as nine to the t over two times nine squared. Similarly, five to the three t can be written as five cubed to the t.

Q: What is the value of nine to the t over two?

Nine to the t over two is equivalent to three to the power of t. This can be determined by using the property that nine to the one half is equal to three. Thus, nine to the t over two becomes three to the t.

Q: How can the expression 10 times 81 times three to the t times 125 to the t power be simplified further?

The expression can be further simplified using the property of multiplying two terms raised to the same power. In this case, three to the t times 125 to the t is equal to three times 125 raised to the t power. Therefore, the expression becomes 810 times three times 125 raised to the t power.

Q: What is the final form of the simplified expression?

The final form of the simplified expression is 810 times three times 125 raised to the t power. It matches the desired form of A times B to the power of t, where A is 810 and B is 375.

Summary & Key Takeaways

• The video demonstrates the process of simplifying a given exponential expression by applying exponent properties.

• The expression is broken down into smaller components, using properties like the product of powers and power of a power.

• The simplified form of the expression is obtained in the form of A times B to the power of t.