Question

Simplify each expression. Assume that no denominator equals 0.

$\frac{{\mathbf{m}}^{\mathbf{7}}{\mathbf{n}}^{\mathbf{4}}\mathbf{p}}{{\mathbf{m}}^{\mathbf{3}}{\mathbf{n}}^{\mathbf{3}}\mathbf{p}}$

Short answer

The required expression is represented by${\mathit{m}}^{\mathbf{4}}\mathit{n}$.

Step-by-step solution

Step 1. Rewrite the provided expression.

Take the help of the identity represented by $\frac{a^m}{a^p}=a^{m-p}$.

$m^{7-3}{n}^{4-3}{p}^{1-1}$

Step 2. Simplify the exponential terms.

Perform subtraction between the exponents.

$m^4{n}^1\cdot 1=m^{4}n$

Step 3. Write the conclusion.

The obtained expression is$m^{4}n$ which cannot be simplified further so it’s the required simplification.