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TestingSnehil1 32 Flashcards 
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Card: 1 / 32 
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What is an exponent? |
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Card: 2 / 32
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An exponent indicates how many times a number (the base) is multiplied by itself. For example, in 2³, the exponent is 3, meaning 2 × 2 × 2 = 8.  |
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Card: 3 / 32
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What is the formula for multiplying powers with the same base? |
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Card: 4 / 32
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When multiplying powers with the same base, add the exponents: aⁿ × aᵐ = aⁿ⁺ᵐ. For example, 2² × 2³ = 2⁵ = 32. |
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Card: 5 / 32
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What is the formula for dividing powers with the same base? |
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Card: 6 / 32
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When dividing powers with the same base, subtract the exponents: aⁿ / aᵐ = aⁿ⁻ᵐ. For example, 5⁴ / 5² = 5² = 25.  |
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Card: 7 / 32
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What does it mean if an exponent is zero? |
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Card: 8 / 32
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Any non-zero base raised to the power of zero equals one: a⁰ = 1 (where a ≠ 0). For instance, 7⁰ = 1. |
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Card: 9 / 32
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How do you simplify a negative exponent? |
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Card: 10 / 32
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A negative exponent indicates the reciprocal of the base raised to the positive exponent: a⁻ⁿ = 1/aⁿ. For example, 3⁻² = 1/3² = 1/9.  |
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Card: 11 / 32
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What is the formula for raising a power to another power? |
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Card: 12 / 32
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When raising a power to another power, multiply the exponents: (aⁿ)ᵐ = aⁿᵐ. For example, (2²)³ = 2⁶ = 64. |
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Card: 13 / 32
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What is the shortcut for simplifying (xy)ⁿ? |
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Card: 14 / 32
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When raising a product to a power, distribute the exponent to each factor: (xy)ⁿ = xⁿyⁿ. For instance, (2*3)² = 2² * 3² = 4 * 9 = 36.  |
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Card: 15 / 32
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Simplify: (x²y³)². |
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Card: 16 / 32
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Using the power of a product rule, (x²y³)² = x⁴y⁶. |
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Card: 17 / 32
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What is the value of 4² × 4⁻³? |
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Card: 18 / 32
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Using the rule for multiplying powers with the same base: 4² × 4⁻³ = 4²⁻³ = 4⁻¹ = 1/4.  |
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Card: 19 / 32
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Evaluate: 27^(1/3). |
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Card: 20 / 32
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The cube root of 27 is 3, since 3³ = 27. |
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Card: 21 / 32
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What is the formula for the product of powers with different bases but same exponents? |
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Card: 22 / 32
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When multiplying different bases with the same exponent, multiply the bases and keep the exponent: aᵐ × bᵐ = (ab)ᵐ. For example, 2² × 3² = (2 × 3)² = 6² = 36.  |
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Card: 23 / 32
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Solve: 2⁴ ÷ 2². |
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Card: 24 / 32
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Using the division rule: 2⁴ ÷ 2² = 2⁴⁻² = 2² = 4. |
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Card: 25 / 32
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What is the result of (3²)(3⁻²)? |
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Card: 26 / 32
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Using the multiplication rule: (3²)(3⁻²) = 3²⁻² = 3⁰ = 1.  |
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Card: 27 / 32
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Find the value of 8^(2/3). |
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Card: 28 / 32
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This is the same as the cube root of 8 squared: (3√8)² = 2² = 4. |
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Card: 29 / 32
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What is the simplified form of 5^(3/4) × 5^(1/4)? |
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Card: 30 / 32
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Using the multiplication rule: 5^(3/4) × 5^(1/4) = 5^(3/4 + 1/4) = 5^(4/4) = 5¹ = 5.  |
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Card: 31 / 32
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Simplify the expression: (x³y²)⁴. |
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Card: 32 / 32
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Using the power of a product rule: (x³y²)⁴ = x^(3×4)y^(2×4) = x¹²y⁸. |
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 Completed! Keep practicing to master all of them. |
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