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# Laws of Exponents

TermDefinition
To multiply exponents with the same base keep the base and add the exponents
To divide exponents with the same base keep the base and subtract the exponents
Write using a positive exponent: a base with a negative exponent in the denominator shift the base to the numerator, while making the exponent positive
Write using a positive exponent: a base with a negative exponent in the numerator shift the base to the denominator, while making the exponent positive
To simplify a power to a power keep the base and multiply the exponents
Any base to the zero power has a value of 1
Evaluate x⁰ 1
Evaluate x⁻³ 1/x³
Evaluate 3⁻² 1/9
Evaluate (4x²)³ 4³x⁶ = 64x⁶
Evaluate (x²y⁶)(3x⁻³y) (3y⁷)/x
Power to a Power Multiply the exponents together and keep the base the same.
8⁷×3⁵×8⁸×2⁴ 8⁴⁹×3⁵
(½)³÷(½)⁵ (½)⁻²
4⁶x16 4⁸
3⁷÷27² 3 or 3¹
(3a²b⁶)⁴ 3⁴a⁸b²⁴ or 81a⁸b²⁴
5⁴a⁶b³÷5²a⁸b 5²a⁻²b² or 25a⁻²b² or 25b²÷a²
Will (-5)⁶ have a positive or negative result? Positive- the exponent is EVEN
Will 6⁵ have a positive or negative result? Positive- the base isn't negative, so we can't have a negative result!
2⁹×32⁴ 2²⁹
15m⁵÷5m³ 3m²