Exponents and Rational Exponents Concepts

The video tutorial covers the rules for working with exponents and rational exponents, focusing on operations with like bases. It begins with an introduction to the concept of exponents and rational exponents. The tutorial then explains how to multiply exponents with like bases by adding the exponents, using examples to illustrate the process. It also covers dividing exponents with like bases by subtracting the exponents, again providing examples to clarify the method. The video emphasizes the importance of converting between radical and rational exponent forms for simplification.

What is the result of multiplying x^5 and x^7 when expressed as a single power of x?

• x^35

• x^12

• x^6

• x^2

How do you express the square root of x^5 using rational exponents?

• x^2/5

• x^5/2

• x^1/5

• x^10

When multiplying x^1/2 and x^2/3, what is the common denominator used to add the exponents?

• 5

• 6

• 2

• 3

What is the simplified form of y^1/3 * y^1/2?

• y^2/3

• y^5/6

• y^1/6

• y^1/5

What operation is performed on exponents when dividing like bases?

• Add the exponents

• Divide the exponents

• Multiply the exponents

• Subtract the exponents

How is the expression (a^5) / (a^2/3) simplified using rational exponents?

• a^5/3

• a^15/6

• a^11/6

• a^3/2

What is the sixth root of a^11 simplified to?

• a^6

• a^1/6

• a^5

• a^11/6

In the expression 6th root of a^11, how many a's are left inside the root after simplification?

• 1

• 5

• 6

• 11

What is the result of subtracting 2/3 from 5/2 in terms of a single power of a?

• a^1/6

• a^11/6

• a^3/2

• a^5/3

What is the simplified form of the expression 6th root of x^7 y^5?

• x^7/6 y^5/6

• x^7 y^5

• x^5 y^7

• x^6 y^5