Question

simplify the expression \\(\left(4r^2t)^3\
ight^2\\). write the variables in alphabetical order.

Explanation:

Step1: Apply power of a power rule

First, multiply the outer exponent by the inner exponent for the entire expression:
$$[(4r^2t)^3]^2 = (4r^2t)^{3 \times 2} = (4r^2t)^6$$

Step2: Distribute exponent to each term

Apply the exponent to the constant and each variable separately using the power of a product rule:
$$(4r^2t)^6 = 4^6 \times (r^2)^6 \times t^6$$

Step3: Calculate each component

Compute the constant power and simplify variable exponents:
$4^6 = 4096$, $(r^2)^6 = r^{2 \times 6} = r^{12}$, $t^6 = t^6$

Step4: Combine terms alphabetically

Arrange variables in alphabetical order ($r$ before $t$):
$$4096r^{12}t^6$$

Answer:

$4096r^{12}t^6$