Question

Simplify. Express your answer using positive exponents.
8u0v
–
1w
–
1
4u
–
7v8w7

Answer 1

To simplify the expression \( \frac{8u^0v}{1w} - \frac{1}{4u^{-7}v^8w^7} \), we can break down the components step by step.

First, notice that \( u^0 = 1 \), so \( 8u^0v = 8v \). Thus, the expression simplifies to:

\[
\frac{8v}{w} - \frac{1}{4u^{-7}v^8w^7}
\]

Next, let's rewrite the second term. Since \( u^{-7} \) can be expressed as \( \frac{1}{u^7} \), we can rewrite \( 4u^{-7}v^8w^7 \) as:

\[
4 \cdot \frac{1}{u^7} \cdot v^8 \cdot w^7 = \frac{4v^8w^7}{u^7}
\]

Consequently, \( \frac{1}{4u^{-7}v^8w^7} \) becomes:

\[
\frac{1}{\frac{4v^8w^7}{u^7}} = \frac{u^7}{4v^8w^7}
\]

Now the expression will look like:

\[
\frac{8v}{w} - \frac{u^7}{4v^8w^7}
\]

Next, we need to find a common denominator for the two fractions. The common denominator will be \( 4v^8w^7 \):

1. The first term can be rewritten with the common denominator:

\[
\frac{8v}{w} = \frac{8v \cdot 4v^7}{4v^8w^7} = \frac{32v^8}{4v^8w}
\]

2. The second term is already:

\[
\frac{u^7}{4v^8w^7}
\]

Now our expression is:

\[
\frac{32v^8 - u^7}{4v^8w^7}
\]

Thus, the final simplified expression is:

\[
\frac{32v^8 - u^7}{4v^8w^7}
\]

This expression is already using positive exponents.