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Laws of Exponent. Math 7. 9 TH GRADE.
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Exponents are used in many algebra problems, so it’s important that you understand the rules for working with exponents.
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Rules for Exponent. Product rule- This says to multiply two exponents with the same base, you keep the base and add the powers Example: a2 • a4 = a6 x8 • x7 = x10.
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Rule 2. 7 TH GRADE. 2. Quotient rule- This says to divide two exponents with the same base, you keep the base and subtract the powers Examples: a^5/a^3 = a^2 y^4/y^9 = y^-5 = 1/y^5.
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3. Negative exponent rule- This says that negative exponent in the numerator gets moved to the denominator and become positive exponents. Negative exponents in the denominator get moved to the numerator and become positive components. Only move the negative exponents. Example: 5^2= 1/5 ^2 = 1/2 5.
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Rule 4. 4. Power rule (power to power)- This says that to raise a power to a power you need to multiply the exponents. Example: (x^5)^4= x^20.
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Rule 5. 5. Zero exponent rule- a0= 1, this says that anything raised to the zero power is 1. Example: 3^0= 1.
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7 TH GRADE. Exponential Notation Base Exponent Expanded form Value Read as 8 ³ 8 3 8x8x8 512 8 to the power of 3 4 ² 4 2 4x4 16 4 to the power of 2 5 ² 5 2 5x5 25 5 to the power of 2 6 ³ 6 3 6x6x6 216 6 to the power of 3 12 ² 12 2 12x12 4 1 2 to the power of 2 7 ² 7 2 7x7 49 7 to the power of 2 10 ⁵ 10 5 10x10x10x 10x10 100,000 10 to the power of 5 6 ⁴ 6 4 6x6x6x6 1,296 6 to the power of 4.