Exploring Rational Exponents in Depth

The video tutorial introduces rational exponents, explaining their equivalence to roots. It covers fractional exponents with examples, demonstrating how to interpret and solve them using a general formula. The tutorial also addresses complex exponent problems, including negative and fractional exponents, providing a comprehensive understanding of the topic.

What does it mean when an exponent is expressed as a fraction?

• It indicates division of the base number.

• It signifies multiplication of the base number.

• It represents a root of the base number.

• It has no mathematical significance.

What does 4 to the power of 1/2 equal?

• 8

• 16

• 2

• 4

What is the equivalent of taking the square root of a number in terms of exponents?

• Raising the number to the power of 4

• Raising the number to the power of 1/2

• Raising the number to the power of 2

• Raising the number to the power of 1/4

How is 16 to the power of 1/2 simplified?

• 2

• 4

• 8

• 16

What does 32 to the power of 3/2 represent?

• The cube root of 32

• The 6th root of 32

• 32 to the power of 6

• The square root of 32 cubed

How can the expression 32^(3/2) be alternatively represented?

• (32^3)^1/2

• 32^(3*1/2)

• 32^3 * 1/2

• 32^(1/2)^3

What is the result of -12/7 + 2/7?

• -10/7

• -14/7

• 10/7

• 14/7

How is 18 to the power of -10/7 simplified?

• 18 to the power of 7/10

• 1 over 18 to the power of 7/10

• 18 to the power of 10/7

• 1 over 18 to the power of 10/7

What does the 7th root of 18 to the power of 10 simplify to?

• 1 over 18 to the power of 10/7

• 18 to the power of 10/7

• 18 to the power of 7/10

• 1 over 18 to the power of 7/10

How is the 4th root of 5 to the power of 7 expressed in exponential form?

• 5 to the power of 4*7

• 5 to the power of 7/4

• 5 to the power of 4/7

• 5 to the power of 7*4