Simplifying Algebraic Expressions with Irrational Exponents

This video tutorial covers the simplification of algebraic expressions, focusing on irrational exponents. It explains the properties of exponents, including multiplication, division, and raising exponents to another power. The tutorial provides examples and applications of these rules, demonstrating how to solve complex problems and simplify expressions effectively.

What is the result of multiplying two terms with the same base, such as x^2 and x^3?

• x^8

• x^6

• x^9

• x^5

When dividing x^5 by x^2, what is the resulting exponent?

• x^5

• x^3

• x^4

• x^2

How do you simplify (x^2)^3?

• x^8

• x^5

• x^9

• x^6

What is the difference between (x^2)^3 and x^(2*3)?

• The first is x^6, the second is x^12

• No difference

• The first is x^8, the second is x^6

• The first is x^6, the second is x^8

How do you simplify 5^(sqrt(2)) * 5^(sqrt(2))?

• 5^4

• 5^2

• 5^(sqrt(4))

• 5^(2*sqrt(2))

What is the result of 9^(1/3) * 9^(1/3)?

• 9^(2/3)

• 9^(1/3)

• 9^(1/2)

• 9^(1)

How do you simplify 8^(1/3) raised to the second power?

• 8^(2/3)

• 8^(1)

• 8^(1/2)

• 8^(1/6)

What is the simplified form of 5^(sqrt(2)) raised to the sqrt(3)?

• 5^(sqrt(6))

• 5^(sqrt(5))

• 5^(sqrt(4))

• 5^(sqrt(3))

How do you simplify 3^(5+2) / 3^(5-2)?

• 3^3

• 3^6

• 3^4

• 3^5

What is the result of simplifying 7^(5+2) / 49?

• 7^5

• 7^7

• 7^8

• 7^6