Simplifying Expressions with Exponents

The video tutorial explains how to simplify an expression using positive exponents. It covers the power to power property, where exponents are multiplied, and the quotient property, where exponents are subtracted. The expression is simplified step-by-step, resulting in a final expression with a positive exponent.

What is the initial expression given in the problem?

• x^3 raised to the power of -5 over x^2 raised to the power of 9

• x^2 raised to the power of 9 over x^3 raised to the power of -5

• x^2 raised to the power of -5 over x^3 raised to the power of 9

• x^3 raised to the power of 9 over x^2 raised to the power of -5

What does the power to power property state?

• (a^m)^n = a^(m+n)

• (a^m)^n = a^(m*n)

• a^m / a^n = a^(m-n)

• a^m * a^n = a^(m+n)

How is the numerator simplified using the power to power property?

• x^27

• x^18

• x^9

• x^3

What is the simplified form of the denominator after applying the power to power property?

• x^10

• x^-5

• x^-10

• x^5

What does the quotient property of exponents state?

• a^m * a^n = a^(m+n)

• a^m / a^n = a^(m-n)

• (a^m)^n = a^(m*n)

• (a^m)^n = a^(m+n)

How do you simplify x^27 divided by x^-10 using the quotient property?

• x^37

• x^17

• x^0

• x^10

What is the result of subtracting a negative exponent?

• It becomes a positive exponent

• It becomes a fraction

• It becomes zero

• It remains negative

What is the final simplified expression?

• x^27

• x^10

• x^17

• x^37

What is the sum of 27 and 10?

• 37

• 27

• 10

• 17

What is the key takeaway from the video?

• Understanding the concept of fractions

• Understanding how to simplify expressions using exponent properties

• Learning how to multiply numbers

• Learning how to add and subtract numbers