Rational Exponents and Radicals

The video tutorial explains how to multiply numbers with rational exponents by focusing on the base and adding exponents. It provides several examples, such as 36 raised to 1/4, 58 raised to 1/2, and 16 raised to 1/8, demonstrating how to simplify these expressions and convert them into radical form. The tutorial also covers adding exponents with different denominators using the LCD method, as shown in the example of 49 raised to 1/3 and 1/6. The video concludes with a practice question for viewers to solve.

What is the first step when multiplying numbers with rational exponents?

• Check if the bases are the same

• Multiply the bases

• Add the exponents directly

• Convert to radical form

When multiplying 36 raised to 1/4 with itself, what is the resulting exponent?

• 1/2

• 2

• 1/4

• 1

How do you simplify 36 raised to 1/2?

• Divide by 2

• Find the square root

• Convert to a cube root

• Multiply by 2

What is the result of 58 raised to 1/2 times 58 raised to 1/2?

• 58 raised to 2

• 58 raised to 1/2

• 58 raised to 1/4

• 58 raised to 1

What is the simplified form of 16 raised to 1/8 times 16 raised to 1/8?

• 16 raised to 1

• 16 raised to 1/16

• 16 raised to 1/4

• 16 raised to 1/2

How do you add exponents with different denominators, like 1/3 and 1/6?

• Multiply the exponents

• Add the numerators directly

• Find the least common denominator

• Use the butterfly method

What is the result of 49 raised to 1/3 times 49 raised to 1/6?

• 49 raised to 1/6

• 49 raised to 1/3

• 49 raised to 1/2

• 49 raised to 1

What is the radical form of 8 raised to 2/3?

• Cube root of 8 squared

• Cube root of 8 cubed

• Square root of 8 cubed

• Fourth root of 8 squared

What is the cube root of 64?

• 2

• 3

• 4

• 5

What is the result of 27 raised to 1/6 times 27 raised to 1/6?

• 27 raised to 1/3

• 27 raised to 1/6

• 27 raised to 1

• 27 raised to 1/2