Question

Express as a power of base 3.

Answer 1

Answer:

3^2

Step-by-step explanation:

a^b^c = a^(b*c)

a^b * a^c = a ^ (b+c)

Lets break down each piece

81^2 = (9*9)^2 = (3^2 *3^2) ^2 = (3^4)^2 = 3^8

9^3 = (3^2) ^3 = 3^(2*3) = 3^6

27^4 = (3*9)^4 = (3*3^2)^4 = (3^(1+2))^4 = (3^3)^4 = 3^3^4 = 3^(3*4) = 3^12

Putting this back into the fraction

3^8 * 3^6

-------------------

3^12

3^(8 +6)

-------------------

3^12

3^14/3^12

a^b/a^c = a^(b-c)

3^(14-12)

3^2

Answer 2

$\text{Use}\\\\(a^n)^m=a^{nm}\\\\a^n\cdot a^m=a^{n+m}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\----------------------\\\\81=3^4\\\\9=3^2\\\\27=3^3\\\\\dfrac{(81^2)(9^3)}{27^4}=\dfrac{(3^4)^2(3^2)^3}{(3^3)^4}=\dfrac{3^{(4)(2)}\cdot3^{(2)(3)}}{{3^{(3)(4)}}}=\dfrac{3^8\cdot3^6}{3^{12}}=\dfrac{3^{8+6}}{3^{12}}\\\\=\dfrac{3^{14}}{3^{12}}=3^{14-12}=3^2\\\\Answer:\ \boxed{\dfrac{(81^2)(9^3)}{27^4}=3^2}$