BackIntro to the Power Rules quiz
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1/15BackSkip to main contentBackWhat does the power rule state for an exponential expression raised to another exponent?
The power rule states that you multiply the exponents when an exponential expression is raised to another exponent. How do you simplify (4^3)^2 using the power rule?
You multiply the exponents: 3 × 2 = 6, so (4^3)^2 = 4^6. What is the simplified form of (-2^3)^5?
The simplified form is -2^(15), since 3 × 5 = 15. How do you evaluate y^8 raised to the 4th power?
Multiply the exponents: 8 × 4 = 32, so y^8^4 = y^32. What does the power of a product rule allow you to do?
It allows you to distribute the exponent to each factor in a product inside parentheses. How do you simplify (3 × 4)^2 using the power of a product rule?
Distribute the exponent: (3 × 4)^2 = 3^2 × 4^2. What is the result of (x × y)^5 using the power of a product rule?
It simplifies to x^5 × y^5. If you have (5 × 3^2)^2, how do you simplify it?
Distribute the exponent: 5^2 × (3^2)^2, then use the power rule to get 5^2 × 3^4. Why is it important to recognize when to apply the power rule or the power of a product rule?
Recognizing when to apply these rules helps simplify exponential expressions efficiently and correctly. What is the value of (5 × 3^2)^2 when fully evaluated?
It equals 2025. How do you rewrite (a × b)^n using the power of a product rule?
You rewrite it as a^n × b^n. What operation does raising a power to another power represent?
It represents multiplying the exponents. What is the simplified form of (x^2 × y^3)^4?
It is x^(2×4) × y^(3×4), or x^8 × y^12. If you see two variables next to each other, like xy, what operation is implied?
Multiplication is implied between the variables. What is the main benefit of using the power and product rules when working with polynomials?
They make it easier to manipulate and simplify expressions with exponents.
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