Simplify. Express your answer using positive exponents. $$ \frac{4 g^{8} h}{4 g^{7} h^{3} \cdot g^{4} h^{6}} $$ $$ \square $$ Submit

Question

UpStudy AI · Accepted Answer

We start with the given expression:

$$
\frac{4 g^{8} h}{4 g^{7} h^{3} \cdot g^{4} h^{6}}
$$

**Step 1: Simplify the Denominator**

Multiply the factors in the denominator:

$$
4 g^{7} h^{3} \cdot g^{4} h^{6} = 4 g^{7+4} h^{3+6} = 4 g^{11} h^{9}
$$

**Step 2: Write the Fraction as a Single Fraction**

Now the expression becomes:

$$
\frac{4 g^8 h}{4 g^{11} h^9}
$$

**Step 3: Cancel Common Factors**

Cancel the factor of $$4$$:

$$
\frac{g^8 h}{g^{11} h^9}
$$

Subtract the exponents for like bases:

$$
g^8 \div g^{11} = g^{8-11} = g^{-3} \quad \text{and} \quad h \div h^9 = h^{1-9} = h^{-8}
$$

**Step 4: Express Using Positive Exponents**

The expression becomes:

$$
g^{-3} h^{-8} = \frac{1}{g^3 h^8}
$$

Thus, the simplified expression is:

$$
\frac{1}{g^{3} h^{8}}
$$
$$ \frac{1}{g^{3} h^{8}} $$

Simplify. Express your answer using positive exponents. \( \frac{4 g^{8} h}{4 g^{7} h^{3} \cdot g^{4} h^{6}} \) \( \square \) Submit