Understanding Exponents and Roots

The video tutorial covers the product of powers, starting with basic multiplication of like bases and moving to more complex examples involving fractional exponents. It explains how to find common denominators to simplify expressions and convert between radical and rational exponent forms. The tutorial provides step-by-step examples to illustrate these concepts, ensuring a clear understanding of exponent rules and simplification techniques.

What is the result when you multiply like bases in exponentiation?

• You add the exponents.

• You multiply the exponents.

• You subtract the exponents.

• You divide the exponents.

How do you simplify 8^(1/2) * 8^(16)?

• 8^(16.5) simplified to 4

• 8^(18)

• 8^(16.5)

• 8^(17)

What is the common denominator used to solve 12^(2/3) * 2^(1/4)?

• 3

• 6

• 12

• 4

What is the cube root of 8?

• 1

• 2

• 3

• 4

What is the simplified form of 8^(2/3)?

• 2

• 16

• 4

• 8

What is the simplified form of 9^(3/2) * 9^(1/4)?

• 9^(7/4)

• 9^(3/4)

• 9^(4/3)

• 9^(5/2)

What is the common denominator for 9^(3/2) and 9^(1/4)?

• 8

• 6

• 4

• 2

When given a problem in radical form, what is a useful first step?

• Convert to decimal form.

• Convert to rational exponents.

• Convert to whole numbers.

• Convert to fractions.

What is the result of 16^(1/3) * 16^(1/5) when simplified?

• 16^(9/15)

• 16^(7/15)

• 16^(6/15)

• 16^(8/15)

What is the first step in solving 16^(1/3) * 16^(1/5)?

• Add the exponents.

• Subtract the exponents.

• Multiply the exponents.

• Find a common denominator.