Power of a Power Law

Laws of Exponent

Mr. Adriel Manansala

​Exponent

​also known as powers/degree, are values that show how many times to multiply a base number by itself.

PRODUCT of POWER LAW

(y²) (y³) = y⁵

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​2⁶ x 2³ =

​When multiplying two bases of the same value, keep the bases the same and then add the exponents together to get the solution.

QUOTIENT of POWER LAW

X⁴ / X² = X²

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12⁶ / 4² =

​When dividing two bases of the same value, keep the base the same, and then subtract the exponent values.

POWER OF A POWER

(x³) ⁴ = x¹²

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(5²)² =

​This rule shows how to solve equations where a power is being raised by another power.

POWER OF A PRODUCT

(xy)² = x² y²

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(3a)³ =

​When any base is being multiplied by an exponent, distribute the exponent to each part of the base.

POWER OF A QUOTIENT

(x / y) ² = x² / y²

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(4 / 2)³ =

​A quotient simply means that you’re dividing two quantities. In this rule, you’re raising a quotient by a power. Like the power of a product rule, the exponent needs to be distributed to all values within the brackets it’s attached to

ZERO EXPONENT

x⁰ = 1

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15⁰ =

​Any base raised to the power of zero is equal to one.

Negative Exponent

x^-2 = 1 / x²

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4^-3 =

​When there is a number being raised by a negative exponent, flip it into a reciprocal to turn the exponent into a positive.