Question

simplify the following expression.
\\((3a^8)^2(-3a^8x^2)^3\\)
show your work here
hint: to add an exponent \\((a^n)\\), type \exponent\ or press \^\

Explanation:

Step1: Expand first term via power rule

$(3a^8)^2 = 3^2 \cdot (a^8)^2 = 9a^{16}$

Step2: Expand second term via power rule

$(-3a^8x^2)^3 = (-3)^3 \cdot (a^8)^3 \cdot (x^2)^3 = -27a^{24}x^6$

Step3: Multiply the two expanded terms

$9a^{16} \cdot (-27a^{24}x^6) = 9 \times (-27) \cdot a^{16+24} \cdot x^6$

Step4: Compute coefficients and exponents

$9 \times (-27) = -243$, $a^{16+24}=a^{40}$

Answer:

$-243a^{40}x^6$