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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 (A)</p> Signup and view all the answers

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

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

Flashcards

Power of a Product Rule

When raising a product to a power, apply the power to each factor individually.

Power of a Power Rule

Raising a power to another power involves multiplying the exponents.

Negative Exponent Rule

To simplify an expression with negative exponents, move the base to the denominator and change the exponent to positive.

Simplifying Exponents

To simplify an expression with a single base and multiple exponents, multiply the exponents together.

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Combining Terms with Exponents

Combine simplified terms with a common base by multiplying the coefficients and keeping the base and exponent.

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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.