Simplify the expression (10st^4u^7)/(5s^9t^3u^8).

Steps to Solve

1. Divide the coefficients

Start by dividing the coefficients (numerical values) in the expression.

The coefficient in the numerator is 10 and in the denominator is 5. So,

$$ \frac{10}{5} = 2 $$

2. Simplify the variable $s$

Next, simplify the variable $s$.

In the numerator, we have $s^1$ (this is implicit as there is no exponent written) and in the denominator, we have $s^9$. So we subtract the exponent in the denominator from the exponent in the numerator:

$$ s^{1-9} = s^{-8} $$

3. Simplify the variable $t$

Now let's simplify the variable $t$.

In the numerator, we have $t^4$ and in the denominator, we have $t^3$. So we subtract the exponent in the denominator from the exponent in the numerator:

$$ t^{4-3} = t^{1} $$

4. Simplify the variable $u$

Next, we simplify the variable $u$.

In the numerator, we have $u^7$ and in the denominator, we have $u^8$. So we subtract again:

$$ u^{7-8} = u^{-1} $$

5. Combine the simplified parts

Now combine all the simplified parts together. The expression becomes:

$$ 2s^{-8}t^{1}u^{-1} $$

6. Rewrite with positive exponents

Since we typically write expressions with positive exponents, we rewrite $s^{-8}$ and $u^{-1}$ as follows:

$$ 2 \cdot \frac{t}{s^8 \cdot u} $$