Question

simplify: $(4^3)^4 \cdot (4^{-2} \cdot 3^0)$
first, simplify $(4^3)^4$.
use the power of a \underline{\hspace{3cm}} property.
to raise an exponential term to a power, \underline{\hspace{3cm}} the exponents.
$(4^3)^4 \cdot (4^{-2} \cdot 3^0) = 4^{\underline{\hspace{0.5cm}}} \cdot (4^{-2} \cdot 3^0)$

Explanation:

Step1: Identify exponent rule

Use the power of a power property.

Step2: Apply power of a power

Multiply the exponents: $(4^3)^4 = 4^{3 \times 4} = 4^{12}$
Expression: $(4^3)^4 \cdot (4^{-2} \cdot 3^0) = 4^{12} \cdot (4^{-2} \cdot 3^0)$

Step3: Simplify zero exponent

Any non-zero number to 0 power is 1: $3^0 = 1$
Expression: $4^{12} \cdot (4^{-2} \cdot 1) = 4^{12} \cdot 4^{-2}$

Step4: Apply product of powers

Add exponents for same base: $4^{12 + (-2)} = 4^{10}$
Expression: $4^{10} = 1048576$

Answer:

1. power
2. multiply
3. $4^{12} \cdot (4^{-2} \cdot 3^0)$

Final simplified form: $4^{10}$ (or 1048576)