Apply the properties of integer exponents to generate equivalent expressions to

Question

(14³•27^-⁷)⁰/3⁴ with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.

Answer 1

To simplify the given expression, let's apply the properties of integer exponents:

1. Product rule: (a^m)(a^n) = a^(m+n)
2. Quotient rule: (a^m)/(a^n) = a^(m-n)
3. Power rule: (a^m)^n = a^(m*n)

First, let's apply the power rule:

(14³ • 27^(-7))^0 / 3^4

Since any non-zero number raised to the power of zero is 1, we have:

1 / 3^4

Now, let's simplify:

1 / 3^4 = 1 / 81

Thus, the simplified expression is 1/81.