Exponent Laws Explained

This video tutorial reviews the properties of exponents, including negative and zero exponents, the product, quotient, and power rules, as well as fractional exponents. The instructor provides explanations and examples for each property, followed by practice problems to reinforce understanding. The video concludes with a summary of the key concepts covered.

What is the equivalent positive exponent form of 3 to the power of -2?

• 1/3^2

• 3^2

• 3^-2

• 1/3^-2

What is the value of any base raised to the power of zero?

• Undefined

• 0

• The base itself

• 1

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

• Subtract the exponents

• Divide the exponents

• Multiply the exponents

• Add the exponents

What is the simplified form of 5^3 * 5^1?

• 5^2

• 5^5

• 5^4

• 5^3

How do you simplify 4^3 / 4^5 using the quotient rule?

• 4^8

• 4^2

• 4^15

• 4^-2

What is the result of (4^3)^2 using the power rule?

• 4^9

• 4^8

• 4^6

• 4^5

What is the simplified form of (3x^2y^3)^3?

• 3x^6y^9

• 9x^5y^6

• 27x^6y^9

• 27x^5y^6

How do you express the cube root of x^4 as a fractional exponent?

• x^(4/1)

• x^(1/3)

• x^(3/4)

• x^(4/3)

What is the simplified form of 4x^(3/2) in radical form?

• 4√(x^3)

• √(4x^3)

• 4x^3

• x^(3/4)

What is the simplified form of 2y^-4 * 4^-3 * x^-3 * y^-15 / (x^3 * y^-3)?

• 1 / (16x^6y^16)

• 1 / (32x^3y^19)

• 1 / (32x^6y^16)

• 1 / (16x^3y^19)