Capstone exponent properties example | Exponent expressions and equations | Algebra I | Khan Academy

TL;DR

Use exponent properties to simplify the equation and find values for a and b that satisfy it.

Transcript

So we have this equation right over here. 12 to the negative 2 power, times 1 over 72 to the fifth power, is equal to 2 to the a power times 3 to the b power. And what I want you to do now is pause this video and find values of a and b that satisfy this equation, where a and b are two integers. And I encourage you to use all of the exponent propert... Read More

Key Insights

• #️⃣ The equation is simplified by expressing numbers as products of powers of prime numbers.
• 🍉 Exponent properties, such as multiplying exponents when there is a common base, are used to manipulate the terms of the equation.
• 🚄 The values of a and b can be found by analyzing the exponents and determining the values that make both sides of the equation equal.

Questions & Answers

Q: How can the equation 12^(-2) * (1/72)^5 = 2^a * 3^b be solved?

To simplify the equation, the speaker breaks down the numbers into products of powers of 2 and 3. By applying exponent properties, the values of a and b can be found.

Q: What is the significance of expressing 12 as 3 times 4?

Expressing 12 as 3 times 4 helps to identify that 3 is a power of 3 and 4 is a power of 2. This simplifies the equation by converting 12 into its prime factorization.

Q: How do you express 1/72 as products of powers of 2 and 3?

To express 1/72 as products of powers of 2 and 3, it can be written as 1/8 times 1/9. 8 is a power of 2, and 9 is a power of 3.

Q: How does the speaker simplify the equation step by step?

The speaker simplifies the equation by manipulating the exponents and applying properties of exponents. By simplifying each term separately and combining like terms, the equation is solved.

Summary & Key Takeaways

• The video explains how to solve an exponential equation by simplifying and manipulating the terms using exponent properties.

• The equation is 12^(-2) * (1/72)^5 = 2^a * 3^b.

• The speaker breaks down the numbers into products of powers of 2 and 3 to simplify the equation.

• By analyzing the exponents and applying exponent properties, the values of a and b are determined to be -19 and -12, respectively.