Exploring Product and Power Rules in Exponents

What operation is performed on the coefficients when using the product rule?

• No operation is performed.

• They are divided.

• They are multiplied together.

• They are added together.

How do you simplify the expression 3x^2 * 2x^4 using the product rule?

• 5x^8

• 6x^6

• 6x^8

• 5x^6

What is the result of x^6 * x^8 according to the product rule?

• x^6

• 2x^14

• x^48

• x^14

When simplifying expressions with the product rule, what do you do with the exponents?

• Add them together

• Divide them

• Subtract them

• Multiply them

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

• 6x^6

• 9x^9

• 6x^5

• 9x^6

According to the power rule, how do you handle a power to a power situation?

• Divide the exponents

• Subtract the exponents

• Multiply the exponents

• Add the exponents

What is the result of (-2)^4 according to the power rule?

• -8

• 8

• -16

• 16

How does a negative base raised to an even exponent affect the sign of the result?

• The result is always negative.

• The result is always positive.

• The sign of the result is unpredictable.

• The result alternates between positive and negative.

What is the simplified form of (-3x^4)^3 using the power rule?

• -81x^12

• 81x^12

• -27x^12

• 27x^12

If a negative base is raised to an odd exponent, what will be the sign of the result?

• Positive

• Negative

• The sign cannot be determined.

• Zero