Exponent Rules and Simplification

This video tutorial covers the properties of exponents, including the multiplication property and raising a power to a power. It begins with a review of basic exponent properties, such as any number raised to the first power equals itself, and the rules for zero and negative exponents. The tutorial then explains how to multiply exponents with the same base by adding the exponents and demonstrates the rule for raising a power to a power by multiplying the exponents. Several examples are provided to illustrate these concepts in practice.

What is the result of any nonzero number raised to the power of zero?

• Zero

• Infinity

• The number itself

• One

If 5x^0 is given, what is the simplified form assuming x is nonzero?

• 0

• 5

• 1

• x

When multiplying two exponents with the same base, what operation is performed on the exponents?

• Add

• Divide

• Subtract

• Multiply

If you have 5x^2 * 7x, what is the simplified form?

• 12x^2

• 35x^3

• 35x^2

• 12x^3

What is the simplified form of (3^4) / (3^2)?

• 3^0

• 3^6

• 3^1

• 3^2

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

• x^5

• x^6

• x^8

• x^9

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

• 2^8

• 2^5

• 2^6

• 2^9

How do you simplify (5x)^2?

• 10x

• 5^2x

• 25x^2

• 5x^2

What is the result of raising a product to a power, such as (ab)^n?

• a^n * b^n

• a^n + b^n

• a * b^n

• a^n * b

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

• x^12y^8

• x^7y^6

• x^3y^8

• x^12y^2