Simplifying Expressions and Exponents

This video tutorial covers the division properties of exponents, explaining how to simplify expressions by subtracting exponents when the bases are the same. It also discusses the implications of negative exponents and demonstrates how to raise a quotient to a power by applying the power to both the numerator and the denominator. The tutorial includes examples to illustrate these concepts.

What is the result of dividing a^m by a^n when the bases are the same?

• a^(m*n)

• a^(n-m)

• a^(m-n)

• a^(m+n)

If you have x^5 divided by x^2, what is the simplified form?

• x^2

• x^10

• x^7

• x^3

What happens if the exponent in the denominator is larger than the exponent in the numerator?

• The result is a negative exponent

• The result is zero

• The result is a positive exponent

• The result is undefined

How do you simplify the expression 4a^10b^5 / 6ab^2?

• 3/2 a^11 b^7

• 2/3 a^11 b^7

• 3/2 a^9 b^3

• 2/3 a^9 b^3

What is the first step in simplifying expressions with multiple variables and coefficients?

• Multiply the coefficients

• Simplify the exponents

• Simplify the coefficients

• Add the exponents

When raising a fraction a/b to the power of n, what is the result?

• a^n * b^n

• a^n / b^n

• a / b^n

• a^n / b

What is the simplified form of (5/7)^2?

• 25/49

• 5/14

• 10/49

• 35/49

How do you simplify (x^5 / y^3)^4?

• x^20 / y^12

• x^9 / y^7

• x^12 / y^20

• x^8 / y^6

What is the result of raising -4 to the power of 2?

• 16

• 8

• -16

• -8

In the expression (-4t^10 / u^6)^2, what is the simplified form of the numerator?

• -8t^20

• 8t^20

• 16t^20

• -16t^20