Simplifying Exponential Expressions

The video tutorial explains how to simplify expressions using the quotient property of exponents. It covers three examples: simplifying x^5/2 divided by x^1/2, t^20/3 divided by t^11/4, and 2^9/2 divided by 2^1/5. The process involves subtracting exponents when the bases are the same and finding a common denominator for fractional exponents. The tutorial emphasizes the importance of understanding the quotient property and applying it correctly to simplify expressions.

What is the result of simplifying x raised to the power of five halves divided by x raised to the power of one half?

• x^0

• x^3

• x^2

• x^1

Which property of exponents is used when dividing expressions with the same base?

• Power Property

• Zero Exponent Property

• Product Property

• Quotient Property

When simplifying t raised to the power of 20/3 divided by t raised to the power of 11/4, what is the least common denominator used?

• 10

• 12

• 8

• 6

What is the simplified form of t raised to the power of 20/3 divided by t raised to the power of 11/4?

• t^(47/12)

• t^(20/3)

• t^(33/12)

• t^(80/12)

Why does the expression t^(47/12) not simplify further?

• 47 is a multiple of 12

• 47 and 12 have no common factors other than 1

• 47 and 12 are both even

• 47 and 12 have a common factor

What is the least common multiple of 2 and 5 used in the final example?

• 20

• 15

• 10

• 5

What is the simplified form of 2 raised to the power of nine halves divided by 2 raised to the power of one fifth?

• 2^(1/5)

• 2^(9/2)

• 2^(45/10)

• 2^(43/10)

Why does the expression 2^(43/10) not simplify further?

• 43 and 10 are both prime

• 43 is a multiple of 10

• 43 and 10 have no common factors other than 1

• 43 and 10 have a common factor

What is the first step in simplifying expressions with different fractional exponents?

• Divide the bases

• Multiply the bases

• Find a common denominator

• Add the exponents

In the context of the video, what does the term 'equivalent fractions' refer to?

• Fractions with the same numerator

• Fractions with the same denominator

• Fractions with the same base

• Fractions with the same value