Question

Express as a power of base 3.

Answer 1

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

Answer 2

3^2

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)

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3^12

3^14/3^12

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

3^(14-12)

3^2