Question

what whole number value of n makes the equation \\(\frac{(27^2)^3 cdot 27^5}{27^n} = 27^2\\) true? use the number pad to enter your answer in the box. n = \\(square\\)

Explanation:

Step1: Simplify the numerator's exponent

$(27^2)^3 = 27^{2\times3}=27^6$

Step2: Combine numerator terms

$27^6 \cdot 27^5 = 27^{6+5}=27^{11}$

Step3: Set up equation for exponents

$\frac{27^{11}}{27^n}=27^2 \implies 11 - n = 2$

Step4: Solve for n

$n = 11 - 2 = 7$

Answer:

7