(3^2)^3 • 3^x = 3^7 • 3^3 / 3^11

Simplify power of a power: First, simplify the left side of the equation by calculating the power of a power. (3^2)^3 = 3^(2*3) = 3^6Rewrite using simplified term: Now, rewrite the left side of the equation using the simplified term. 3^6 • 3^x = 3^(6+x)Combine and divide powers: Next, simplify the right side of the equation by combining the powers of 3 that are being multiplied and then dividing. 3^7 • 3^3 / 3^11 = 3^(7+3) / 3^11 = 3^10 / 3^11Simplify division of powers: Now, simplify the division of powers on the right side by subtracting the exponents. 3^10 / 3^11 = 3^(10-11) = 3^(-1)Set exponents equal: We now have the simplified equation: 3^(6+x) = 3^(-1) Since the bases are the same, we can set the exponents equal to each other. 6 + x = -1Solve for x: Finally, solve for x by subtracting 6 from both sides of the equation. x = -1 - 6 x = -7

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Factor by grouping

Full solution

(3^2)^3 \cdot 3^x = 3^7 \cdot \frac{3^3}{3^{11}}

Simplify power of a power: First, simplify the left side of the equation by calculating the power of a power. $\newline$ $(3^2)^3 = 3^{(2*3)} = 3^6$
Rewrite using simplified term: Now, rewrite the left side of the equation using the simplified term. $3^6 \cdot 3^x = 3^{6+x}$
Combine and divide powers: Next, simplify the right side of the equation by combining the powers of $3$ that are being multiplied and then dividing. $\frac{3^7 \cdot 3^3}{3^{11}} = \frac{3^{7+3}}{3^{11}} = \frac{3^{10}}{3^{11}}$
Simplify division of powers: Now, simplify the division of powers on the right side by subtracting the exponents. $3^{10} / 3^{11} = 3^{(10-11)} = 3^{-1}$
Set exponents equal: We now have the simplified equation: $\newline$ $3^{6+x} = 3^{-1}$ $\newline$ Since the bases are the same, we can set the exponents equal to each other. $\newline$ $6 + x = -1$
Solve for x: Finally, solve for x by subtracting $6$ from both sides of the equation. $\newline$ $x = -1 - 6$ $\newline$ $x = -7$