Exponents and Their Properties

This video tutorial explains operations with rational exponents, including addition, subtraction, multiplication, and division. It covers how to break down exponents into smaller parts, use radicals, and apply properties like the associative and commutative properties. The tutorial provides specific examples to illustrate these concepts, focusing on simplifying terms with rational exponents and understanding the relationship between fractional exponents and radicals.

What must be true about the figures when adding or subtracting numbers with exponents?

• They must be different sizes.

• They must have the same coefficient.

• They must have the same base and dimensions.

• They must be in radical form.

How can two to the one-third be expressed using a radical?

• As the fourth root of two.

• As the cube root of two.

• As the fifth root of two.

• As the square root of two.

What happens when you add x to the one-half three times?

• You get x to the three-halves.

• You get three x to the one-half.

• You get x to the one-third.

• You get three x squared.

When multiplying figures with different dimensions, what must be done with the exponents?

• Subtract them.

• Multiply them.

• Divide them.

• Add them.

What is the result of multiplying nine to the one-half three times?

• Eighteen

• Twenty-seven

• Nine

• Thirty-six

How can 16 to the three-fourths be simplified?

• As 4

• As 8

• As 2

• As 16

What property allows you to change the order of factors in multiplication?

• Identity property

• Commutative property

• Distributive property

• Associative property

What is the result of multiplying two c to the three-fifths by two c to the two-fifths?

• 2c

• 8c

• 6c

• 4c

How can you express four times c to the four-fifths using a radical?

• As the fifth root of c to the fourth

• As the fourth root of c to the fifth

• As the square root of c to the fourth

• As the cube root of c to the fifth

What is the base in the expression 16 to the three-fourths?

• 3

• 4

• 1

• 16