Simplifying Expressions with Negative Exponents

This video tutorial explains how to simplify expressions with negative exponents. It begins with an introduction to negative exponents, explaining that a negative exponent indicates the reciprocal of the base raised to the positive exponent. The video then provides three examples: the first demonstrates simplifying a single term with a negative exponent, the second uses the product rule to combine terms with the same base, and the third applies the power of powers rule to an expression with multiple terms. Each example emphasizes converting negative exponents to positive by moving them to the denominator.

What does a negative exponent indicate?

• The number should be squared.

• The number should be divided by itself.

• The number should be multiplied by itself.

• The number should be moved to the denominator.

How is a^(-n) simplified?

• n/a

• a^(-n)

• 1/a^n

• a^n

In the expression 4x^(-3)y^5, what happens to x^(-3)?

• It stays in the numerator.

• It moves to the denominator as x^3.

• It is eliminated.

• It becomes x^3.

What remains unchanged in the expression 4x^(-3)y^5?

• 4 and x^(-3)

• x^(-3)

• y^5 and x^(-3)

• 4 and y^5

When multiplying 3a^(-4) and 4a^2, what is the first step?

• Divide the coefficients.

• Add the exponents.

• Multiply the coefficients.

• Subtract the exponents.

What is the result of adding the exponents in 3a^(-4) * 4a^2?

• a^2

• a^(-2)

• a^6

• a^(-6)

In the expression 3a^(-4) * 4a^2, what happens to a^(-2)?

• It is eliminated.

• It stays in the numerator.

• It becomes a^2.

• It moves to the denominator as a^2.

What does the power of powers rule state?

• Divide the exponents.

• Multiply the exponents.

• Add the exponents.

• Subtract the exponents.

How is (2a^2b^(-2))^(-2) simplified initially?

• 1/(2a^2b^2)

• 1/(2a^2b^(-2))^2

• 2a^4b^(-4)

• 2a^(-4)b^4

What is the final simplified form of (2a^2b^(-2))^(-2)?

• 1/(4a^(-4)b^(-2))

• 4a^(-4)b^(-2)

• 1/(4a^4b^2)

• 4a^4b^2