Exponent Rules and Simplification

The video tutorial explains how to simplify mathematical expressions using positive exponents. It covers multiplication of terms with the same base by adding exponents, raising powers to powers by multiplying exponents, and dividing expressions by subtracting exponents. The tutorial also addresses handling negative exponents by converting them to positive exponents in fraction form. Each example is broken down step-by-step to ensure understanding.

What is the simplified form of 3x²y³ × 7x⁴y³?

• 10x⁶y⁹

• 21x⁶y⁶

• 21x⁶y⁹

• 10x⁶y⁶

When multiplying terms with the same base, what do you do with the exponents?

• Add them

• Multiply them

• Subtract them

• Divide them

What is the result of (4x⁵y³)²?

• 8x⁵y³

• 8x¹⁰y⁶

• 16x¹⁰y⁶

• 16x⁵y⁶

How do you simplify an expression when raising a power to another power?

• Divide the exponents

• Multiply the exponents

• Add the exponents

• Subtract the exponents

What is the simplified form of 21x⁶y³ ÷ 7x⁴y⁷?

• 3x²y⁴

• 3x²/y⁴

• 3x⁴/y²

• 3x⁴y²

When dividing terms with the same base, what operation is performed on the exponents?

• Subtract them

• Divide them

• Multiply them

• Add them

How do you handle a negative exponent in a simplified expression?

• Leave it as is

• Add 1 to the exponent

• Move the base to the opposite side of the fraction

• Subtract 1 from the exponent

What is the simplified form of 2x⁻³y⁴?

• 2x⁻³y⁴

• 2x³y⁴

• 2y⁴x³

• 2y⁴/x³

In the expression 2x⁻³y⁴, which part of the expression is not simplified?

• The entire expression is simplified

• The coefficient 2

• The base x with a negative exponent

• The base y with a positive exponent

What happens to the exponent when you move a base across the fraction bar?

• It changes sign

• It becomes zero

• It doubles

• It remains the same