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Exponent Rule Application

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Questions and Answers

What is the first step to simplify the expression (x²y³)^(-2)?

Distribute the exponent -2 to each part (correct)

Express the result with positive exponents

Combine the terms

Apply the power rule for exponents

After applying the power of a product rule, what is the expression transformed into?

(x^2 * y^3)^(-2)

(x^2)^(-2) * (y^3)^(-2) (correct)

(x^2y^3)^2

(x^(-2) * y^(-3))^2

What is the result of applying the power rule to the expression x^(2 * -2)?

x^(-2)

x^4

x^(-4) (correct)

x^2

How can the expression x^(-4) be rewritten using positive exponents?

<p>1/x^4</p> Signup and view all the answers

What is the final simplified form of the expression (x²y³)^(-2)?

<p>1/(x^4y^6)</p> Signup and view all the answers

Study Notes

Exponent Rule Application

To simplify the expression (x²y³)^(-2), use the power of a product rule: (ab)^n = a^n * b^n. Apply this rule to both x and y terms within the parentheses.
Distribute the exponent -2 to each part within the brackets: (x²)⁻² * (y³)^⁻²
Apply the power rule for exponents: (a^m)^n = a^(m*n) x^(2 * -2) * y^(3 * -2)
Simplify the exponents: x^(-4) * y^(-6)
To express the result with positive exponents, use the rule a⁻ⁿ = 1/aⁿ: 1/x⁴ * 1/y⁶
Combine the terms: 1/(x⁴y⁶)

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Description

This quiz covers the application of exponent rules, specifically focusing on simplifying expressions with negative exponents. Participants will practice the power of a product rule and learn how to express results with positive exponents. This is essential for mastering concepts in algebra.