Converting Rational Exponents and Radicals: Key Concepts and Techniques

The video tutorial covers the basics of exponents, including how to handle positive, negative, and fractional exponents. It emphasizes understanding over memorization and uses examples to explain the concept of fractional exponents, which relate to roots. The tutorial also highlights common mistakes and provides advanced examples to solidify understanding.

What should you do if you have an exponent of negative five?

• Add five to the base

• Subtract five from the base

• Multiply the base by itself five times

• Take the reciprocal and multiply the base by itself five times

What does 9 to the 1/2 power represent?

• Multiplying 9 by itself half a time

• The square root of 9

• Nine divided by two

• Nine times two

What is the result of squaring the number that represents 9 to the 1/2 power?

• 27

• 3

• 9

• 81

What does a to the 1/n power represent?

• a raised to the nth power

• a divided by n

• The nth root of a

• a multiplied by n

How can you simplify 8 to the 2/3 power?

• 8 to the 1/3 power squared

• 8 cubed and then squared

• 8 squared and then cubed

• 8 to the 1/2 power cubed

What is the cube root of 8?

• 3

• 4

• 2

• 8

What is a common mistake when dealing with fractional exponents?

• Multiplying the base by the exponent

• Taking the reciprocal of the base

• Adding the base to the exponent

• Flipping the base and exponent

How do you simplify 3x to the -1/2 power?

• 1 over the square root of 3x

• 3x squared

• 3x to the 1/2 power

• 1 over 3x squared

What is the result of adding the exponents 1/2 and 1/3?

• 1/5

• 2/5

• 5/6

• 3/5

How can you express the sixth root of 2 raised to the fifth power?

• 2 to the 1/5 power

• 2 to the 1/6 power

• 2 to the 6/5 power

• 2 to the 5/6 power