Question

Question
Apply the Properties of Integer Exponents to generate equivalent expressions to (143⋅27−7)034
with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
(143⋅27−7)034=

Answer 1

To simplify the expression \((143 \cdot 27^{-7})^{034}\) using the properties of integer exponents, we first note that \(034\) is simply \(34\). So we can rewrite the expression as:

\[
(143 \cdot 27^{-7})^{34}
\]

Next, we can apply the property of exponents that states \((a \cdot b)^n = a^n \cdot b^n\). This gives us:

\[
(143)^{34} \cdot (27^{-7})^{34}
\]

Next, we handle the term \((27^{-7})^{34}\) using the property \((a^m)^n = a^{m \cdot n}\):

\[
(27^{-7})^{34} = 27^{-7 \cdot 34} = 27^{-238}
\]

Now, we can put everything together:

\[
(143)^{34} \cdot 27^{-238}
\]

To eliminate the negative exponent and write it in terms of positive exponents, we use the property \(a^{-n} = \frac{1}{a^n}\):

\[
(143)^{34} \cdot \frac{1}{27^{238}} = \frac{(143)^{34}}{27^{238}}
\]

Now, we have an equivalent expression with only positive exponents:

\[
\frac{(143)^{34}}{27^{238}}
\]

Next, we check if these numbers can be simplified further.

**Final Result:**

\[
\frac{(143)^{34}}{27^{238}}
\]

This is the simplified expression in the form of a fraction with no remaining exponents.

Thus, the final answer is:

\[
\frac{(143)^{34}}{27^{238}}
\]