Understanding the Third Law of Exponents

The video tutorial explains the third law of exponents, which states that for any real number x and positive integers m and n, x raised to m raised to n equals x raised to m times n. The video provides examples with integer and rational bases to illustrate this law.

What is the main topic discussed in this video?

• The first law of exponents

• The second law of exponents

• The third law of exponents

• The fourth law of exponents

According to the third law of exponents, if x is a real number and m, n are positive integers, how can x raised to m raised to n be expressed?

• x raised to m plus n

• x raised to m times n

• x raised to n minus m

• x raised to m divided by n

Which of the following is equivalent to (x^m)^n according to the third law of exponents?

• x^(m/n)

• x^(m*n)

• x^(m-n)

• x^(m+n)

In the first example, what is the base number used?

• 2

• 3

• 5

• 6

In the example with integers, what is the final exponent of 5?

• 9

• 6

• 5

• 3

What is the initial expression given in the first example?

• 5 raised to 2 raised to 3

• 2 raised to 5 raised to 3

• 3 raised to 5 raised to 2

• 5 raised to 3 raised to 2

In the second example, what is the base of the rational number?

• 1/2

• 3/4

• 4/5

• 2/3

What is the final exponent of the rational number in the second example?

• 10

• 5

• 20

• 15

In the second example, what are the two powers applied to the rational number?

• 2 and 3

• 3 and 5

• 5 and 3

• 5 and 2

How is the expression (2/3)^5^3 simplified using the third law of exponents?

• (2/3)^8

• (2/3)^15

• (2/3)^10

• (2/3)^5