Question

next, simplify 3^0.
use the ____________ exponent property.
= 4^12 · (4^-2 · 3^0)
= 4^12 · (4^-2 · _______)
then, simplify 4^-2 · 1.
= 4^12 · (4^-2 · 1)
= 4^12 · _______
last, simplify 4^12 · 4^-2.
use the product of ____________ property.
= 4^12 · 4^-2
= 4^{— + —}
= 4^{—}

Explanation:

Step1: Apply zero exponent rule

Any non-zero number to the 0 power is 1: $3^0 = 1$

Step2: Simplify $4^{-2} \cdot 1$

A number times 1 is itself: $4^{-2} \cdot 1 = 4^{-2}$

Step3: Identify product of powers rule

For same bases, add exponents: $a^m \cdot a^n = a^{m+n}$

Step4: Substitute exponents into rule

$4^{12} \cdot 4^{-2} = 4^{12 + (-2)}$

Step5: Calculate the final exponent

$12 + (-2) = 10$, so $4^{10}$

Answer:

1. Use the zero exponent property.

$= 4^{12} \cdot (4^{-2} \cdot \boldsymbol{1})$

1. $= 4^{12} \cdot \boldsymbol{4^{-2}}$
2. Use the product of powers property.

$= 4^{\boldsymbol{12} + \boldsymbol{(-2)}}$
$= 4^{\boldsymbol{10}}$