Exploring Laws of Exponents: Power of Product & Quotient

This video tutorial covers two laws of exponents: the power of a product and the power of a quotient. It explains how to apply these rules with examples, including handling negative exponents. The power of a product rule involves raising each factor in a product to a power, while the power of a quotient rule involves raising both the numerator and denominator to a power. The video also highlights common mistakes, such as incorrectly applying these rules to sums instead of products or quotients.

If you have the expression (5x * y^2)^2, what is the result for y?

• 2y

• y^8

• y^4

• y^2

What does the power of a product rule allow you to do with the exponents?

• Add exponents of the factors

• Multiply exponents of the factors

• Raise each factor inside the parentheses to the given power

• Subtract exponents of the factors

What is the result of (a^2 * b^4)^3 for a?

• a^12

• a^24

• a^8

• a^6

How do you handle a negative base, like (-2) when raised to an even power?

• It becomes positive

• It remains negative

• It becomes zero

• It is undefined

What is the result of cubing the fraction (2x/y^2)?

• 6x^3/y^6

• 8x/y^6

• 8x^3/y^8

• 8x^3/y^6

In the power of a quotient rule, what happens to the exponents of the numerator and the denominator?

• They are multiplied together

• Each is raised to the power independently

• They are subtracted from each other

• They are added together

If you have the expression (2/3)^2, what is the result?

• 2/6

• 4/6

• 1/9

• 4/9

What is the result of cubing 2m^7n^5 in the numerator of a fraction?

• 8m^21n^15

• 8m^15n^21

• 6m^21n^15

• 8m^7n^5

How do you simplify a fraction raised to a negative exponent?

• Flip the fraction and change the sign of the exponent

• Multiply the exponents by -1

• Add the exponents

• Subtract the exponents

What is the simplified form of (4x^3/5)^-2?

• 16/25x^6

• 25x^6/16

• 16x^6/25

• 25/16x^6