Apply All Exponent Rules Practice

Question

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Question
Apply the Properties of Integer Exponents to generate equivalent expressions to (14^3⋅27^−7)0^/3^4
with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
(14^3⋅27^−7)^0/3^4=

Answer 1

To solve the expression \((14^3 \cdot 27^{-7})^0 / 3^4\), let's apply the properties of exponents:

1. Exponent Rule for Zero: Any non-zero expression raised to the power of zero is equal to 1. Therefore, \((14^3 \cdot 27^{-7})^0 = 1\).

Now the expression simplifies to:

\[ \frac{1}{3^4} \]

2. Calculate \(3^4\):

\[ 3^4 = 3 \cdot 3 \cdot 3 \cdot 3 = 81 \]

So, we now have:

\[ \frac{1}{81} \]

Thus, the final simplified expression with no remaining exponents is:

\[ \frac{1}{81} \]