What I Have Learned About Grade 9 Exponents

I have learned that the exponent of a number says how many times to use the number in a multiplication. It tells you to make copies of the base.

For example: $4^2$

The large number which is 4 is what we call the base, while on the top right of it is what we call the exponent or the power.

The second power tells that the base should be multiplied twice. Evaluating the exponent:

$4^2$ = 4 x 4

=16

How do brackets affect evaluating a power?

If there’s a negative number(-) in the brackets, it’s considered that the base and the sign are together, but if there are no brackets, the exponent will only consider the negative number as a positive because the exponent thinks the negative sign is a “minus” sign.

An example with the brackets:

$(-3)^4$ = (-3)(-3)(-3)(-3) = +81

An example without the brackets:

$-3^4$ = -(3)(3)(3)(3) = -1(3)(3)(3)(3) = (-1)(81) = -81

Multiplication Law: If the bases are the same, they are considered as the multiplication law. In this law, the bases don’t multiply while the exponents add together. However, if the bases don’t match you do the BEDMAS.

For example: $6^3\cdot6^7$ = $6^{10}$

Division Law: This law is a bit similar to the multiplication law like if the bases match, you add the powers but in this law, you subtract the exponents instead of adding them together.

For Example: $6^3 \div 6^2$ = $6$

Power of a Power Law is when a power is in the brackets and another power outside. In this law, you have to multiply the exponents.

For example:

$(7^5)^3$ = $7^{5 \cdot3}$ = $7^{15}$

Zero Exponent Law is when any base has a power is zero, it is equal to one, because if you’re going to divide something like this: $4 \div 4$ = 1 and since this is zero exponent, there’s should be an invisible 1 on both numbers.