Exponents and Their Properties

The video tutorial explains how to simplify an algebraic expression using the power rule of exponents. It begins by introducing the expression and then explains the power rule with examples. The tutorial applies the rule to the given problem, breaking down the expression and calculating the powers of numbers involved. Finally, it simplifies the expression to its simplest form.

What is the property used to simplify an expression like (x/y)^n?

• x^n - y^n

• x^n + y^n

• x^n / y^n

• x^n * y^n

In the example given, what is (x/y)^3 equivalent to?

• x^3 / y^3

• x^3 * y^3

• x^3 + y^3

• x^3 - y^3

How do you express (2a^2)^4 using the exponentiation property?

• 2^4 / a^8

• 2^4 + a^8

• 2^4 * a^8

• 2^4 - a^8

What is the value of 2^4?

• 16

• 8

• 4

• 32

What is the value of 3^4?

• 81

• 243

• 27

• 9

What is the power rule of exponents used in the simplification?

• x^(n-m)

• x^(n+m)

• x^(n*m)

• x^(n/m)

How do you simplify a^2 raised to the 4th power?

• a^6

• a^16

• a^8

• a^4

What is the simplified form of b^5 raised to the 4th power?

• b^20

• b^9

• b^25

• b^10

What is the final simplified form of the expression 2a^2 / 3b^5 all raised to the 4th power?

• 16a^8 - 81b^20

• 16a^8 + 81b^20

• 16a^8 * 81b^20

• 16a^8 / 81b^20

What is the result of multiplying 5 by 4 in the context of the power rule?

• 20

• 10

• 25

• 9