Notes

Good day everyone! My name is Angeline A. Nicolas from grade 8-Cassiopoeia. This day I am going to tackle the law of exponent by giving and explaining each rule and provide examples.

The first rule is the Multiplication Rule, it is easy to remember its rule by adding its exponent. Simply, add the exponent that the term has.

For example , x² × x⁵ by having same base we can simply add its exponent. So, x² × x⁵ is equal to x⁷. Since, 2+5 is equal to 7.

Second is the Division Rule, divison rule is different from the multimplication rule. In division rule we must know the difference of exponent of each terms. Simply, it is an opposite of multiplication rule.

For example, y⁵÷y² by having same base you can minus the exponent directly. So, y⁵÷y² is equal to y³. Since 5 minus 2 is equal to 3.

Third is the Power of a Power Rule, the power rule says that if we have an exponent raised to another exponent, you can just multiply the exponents together. For example, (2²)³.
We can rewrite this form as 2²•3 that is equal to 2⁶ since we multiply the exponent (2 and 3). But thats not the final answer since we have the exponent of 6. To answer this multimply the 2 by six times and you will get 64.
Angeline
Angeline Nicolas
Fourth is the Power of a Product Rule, this rule tells us that we can simplify a power of a power by multiplying the exponents and keeping the same base. For example, (2x²)⁴.
To simplify this we must distribute the exponent outside to the numbers in the parenthesis. (2x²)⁴ can rewrite as 8x⁸. Since we multiply the exponent 4 to the coefficient 2 and literal coefficient x².

Fifth is the Power of a Fraction Rule, wherein a quotient is raised to a power, the result is quotient of the numerator to the power and the denomiator to the power. Example is (3/×)² = 3²/x² = 9/x²

Sixth is the zero exponent, any number that has a power of zero is equal to 1. For example, 1⁰, 2⁰, 3⁰ and so on.

Seventh is the Negative Exponent, tells us that a number with a negative exponent should be put to the denominator, adnd vice verca. For example you see x^-4 , it actually stands for 1/x4

Lastly is the Fractional Exponent, it is when you have fractional exponent, the numerator is the power and the denominator is the root. For example, 2¾ is equal to fourth root of 2 cube.