Exponent Rules and Simplification

The video tutorial explains how to simplify expressions involving fractions raised to powers using exponent rules. It covers two main rules: raising both the numerator and denominator to the power, and multiplying exponents when powers are raised to powers. The tutorial provides three examples to illustrate these rules, demonstrating the simplification process step-by-step. The importance of understanding these rules is emphasized, especially when dealing with negative exponents.

What is the first step in simplifying expressions involving fractions raised to powers?

• Add the exponents of the numerator and denominator.

• Subtract the exponents of the numerator and denominator.

• Multiply the exponents of the numerator and denominator.

• Divide the exponents of the numerator and denominator.

According to the basic exponent rule, how do you simplify (x/y)^n?

• x^n + y^n

• x^n - y^n

• x^n * y^n

• x^n / y^n

When simplifying (x^a/y^b)^n, what operation is performed on the exponents?

• Multiplication

• Subtraction

• Addition

• Division

What is the result of (2/3)^2 using exponent rules?

• 1/9

• 8/27

• 4/9

• 2/3

In the expression (2/3)^2, what is the exponent of the numerator after simplification?

• 1

• 4

• 2

• 3

How do you simplify (x/4)^3 using exponent rules?

• x^3 - 4^3

• x^3 + 4^3

• x^3 * 4^3

• x^3 / 4^3

What is the result of 4^3?

• 32

• 128

• 64

• 16

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

• y^4 * 2^6

• y^4 / 2^6

• y^4 + 2^6

• y^4 - 2^6

What is the value of 2^6?

• 256

• 128

• 64

• 32

How do you evaluate 2^6 using a calculator?

• Enter 2, press the multiplication key, enter 6, and press equals.

• Enter 2, press the exponent key, enter 6, and press equals.

• Enter 6, press the exponent key, enter 2, and press equals.

• Enter 6, press the multiplication key, enter 2, and press equals.