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Identity Exponent
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Any base raised to the power of 1 remains the same.
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x1 = x
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71 = 7
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Product of Powers
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When multiplying two expressions with the same base, add the exponents.
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xm·xn = xm + n
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x3·x2 = x3 + 2 = x5
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Quotient of Powers
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When dividing two expressions with the same base, subtract the exponents.
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where x ≠ 0
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Power of a Power
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When raising a power to another power, multiply the exponents.
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(xm)n = xm · n
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(x3)2 = x3 · 2 = x6
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Power of a Product
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When raising a product to an exponent, distribute the exponent to each factor in the product.
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(2x)m = 2m · xm
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(2x)3 = 23 · x3 = 8x3
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Power of a Quotient
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When raising a quotient to an exponent, apply the exponent to both the numerator and the denominator.
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where y ≠ 0
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Zero Exponent
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Any non-zero base raised to the power of zero is equal to 1.
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x0 = 1
where x ≠ 0
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90 = 1
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Negative Exponent
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A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent.
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where x ≠ 0
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Exporting the Cheat Sheet to PDF
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- Click on the Printer friendly link (here or above the table).
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