Simplifying Expressions with Exponents

The video tutorial explains how to simplify expressions using the power and product properties of exponents. It covers two examples: the first involves simplifying y to the third times y squared raised to the sixth power, resulting in y to the fifteenth. The second example simplifies x to the fourth times x cubed squared over 4x to the seventh, resulting in x to the third divided by four. The tutorial emphasizes the importance of understanding exponent rules, such as multiplying and adding exponents, and provides step-by-step guidance for each example.

What is the first step in simplifying an expression with exponents?

• Add the exponents

• Divide the exponents

• Multiply the exponents

• Use the power property

If you have y^3 * y^2 raised to the 6th power, what is the result of applying the power property?

• y^5

• y^18

• y^12

• y^15

After applying the power property, what is the next step to simplify y^3 * y^12?

• Subtract the exponents

• Divide the exponents

• Add the exponents

• Multiply the exponents

What is the simplified form of y^3 * y^12?

• y^6

• y^18

• y^15

• y^9

How do you simplify x^3 squared in the expression x^4 * x^3 squared?

• x^8

• x^7

• x^9

• x^6

What is the result of simplifying x^4 * x^6?

• x^9

• x^10

• x^8

• x^12

What is the coefficient of x^10 in the expression x^10 / 4x^7?

• 1

• 4

• 7

• 1/4

How do you simplify the expression x^10 / x^7?

• x^10

• x^7

• x^3

• x^17

What is the final simplified form of the expression x^10 / 4x^7?

• 4x^3

• x^3 / 4

• x^7 / 4

• 4 / x^3

Which property of exponents is used to simplify x^10 / x^7?

• Power property

• Product property

• Quotient property

• Zero exponent property