Exploring Rational Expressions in Math 10C

The video tutorial covers various exponent laws, including the product, quotient, power of a product, power of a quotient, and power of a power laws. It demonstrates how to simplify expressions using these laws, with examples involving both positive and negative exponents. The tutorial also addresses common mistakes and provides strategies for simplifying complex expressions. Students are encouraged to practice these concepts to gain a deeper understanding.

What is the product law of exponents?

• Add the exponents when the bases are the same.

• Multiply the exponents when the bases are different.

• Divide the exponents when the bases are different.

• Subtract the exponents when the bases are the same.

Which student correctly simplified the expression 3x^2 * 5x^3?

• Harry: 8x^10

• Janet: 16x^6

• None of the above

• Laura: 15x^5

How do you simplify the expression 68a^6 / 3a^2?

• 22a^4

• 23a^4

• 23a^3

• 22a^3

What is the result of (4x^5 * 2x^3)?

• 6x^15

• 8x^15

• 6x^8

• 8x^8

What is the simplified form of (7a^8 * 6a^12) / (5a^5)?

• 42a^10

• 42a^5

• 42a^20

• 42a^15

How do you handle negative exponents in a fraction?

• Only the numerator becomes negative.

• The negative exponent applies to the entire fraction.

• Both numerator and denominator become negative.

• Only the denominator becomes negative.

What is the simplified form of (3x^2)^3?

• 9x^6

• 27x^6

• 9x^9

• 27x^9

What is the result of (2a^3)^4?

• 16a^7

• 8a^7

• 16a^12

• 8a^12

How do you simplify (x^2 * y^3)^4?

• x^6 * y^12

• x^6 * y^7

• x^8 * y^12

• x^8 * y^7

What is the simplified form of (5x^3 / 2x^2)^2?

• 25x^2 / 4

• 25x^4 / 4

• 25x^2 / 2

• 25x^4 / 2