Understanding Exponents and Simplification

The video tutorial explains how to simplify an expression with exponents by applying the power to power property and converting negative exponents to positive ones. It starts with an expression involving x and y raised to negative powers and demonstrates how to multiply exponents when raising a power to another power. The tutorial then shows how to rewrite the expression using only positive exponents by moving terms with negative exponents to the denominator, resulting in a simplified expression.

What is the initial expression that needs to be simplified?

• x^7 y^5 raised to the power of -3

• x^7 y^5 raised to the power of 3

• x^5 y^7 raised to the power of 3

• x^5 y^7 raised to the power of -3

What does the power to power property of exponents state?

• Divide the exponents

• Subtract the exponents

• Add the exponents

• Multiply the exponents

How do you calculate the new exponent for x in the expression?

• 7 / (-3)

• 7 - (-3)

• 7 + (-3)

• 7 * (-3)

What is the result of x raised to the power of 7 times -3?

• x^10

• x^-21

• x^-10

• x^21

What is the exponent property used to convert negative exponents to positive?

• a^-m = 1/a^m

• a^m = a^-m

• a^m = 1/a^-m

• a^-m = a^m

How can you rewrite a^-m to make the exponent positive?

• a^-m = 1/a^-m

• a^-m = a^-m

• a^-m = 1/a^m

• a^-m = a^m

What is the final expression using only positive exponents?

• 1/(x^-21 y^-15)

• x^-21 y^-15

• 1/(x^21 y^15)

• x^21 y^15

What happens to the sign of the exponent when moving a^-m to the denominator?

• It becomes positive

• It becomes negative

• It remains the same

• It doubles

Why is it important to express exponents positively?

• It simplifies calculations

• It is a mathematical rule

• It complicates the expression

• It is unnecessary