Question

Evaluate the expression below.

$\frac{5^3\times 4^2-5^2\times 4^3}{5\times 4}$

Short answer

The value of the given expression is 20

i.e.

$\frac{5^3\times 4^2{\text{-5}}^2\times 4^3}{5\times 4}=20$

Step-by-step solution

Step 1. Given Information.

Given that, the expression is-

$\frac{5^3\times 4^2{\text{-5}}^2\times 4^3}{5\times 4}$

Step 2. Concept Used.

Before solving the whole expression

Firstly, write the values of$5^3,4^2,5^2,4^3,$

Now,

role="math" localid="1641978690240" $$\begin{gathered} 5^3=5\times 5\times 5 \\ =125 \\ {4}^2=4\times 4 \\ =16 \\ {5}^2=5\times 5 \\ =25 \\ {4}^3=4\times 4\times 4 \\ =64 \end{gathered}$$

Step 3. Evaluate the given expression.

$$\begin{gathered} \frac{5^3\times 4^2{\text{-5}}^2\times 4^3}{5\times 4}\text{=}\frac{125\times 16\text{-25}\times \text{64}}{20} \\ \text{=}\frac{2000\text{-1600}}{20} \\ \text{=}\frac{400}{20} \end{gathered}$$

Therefore,

$\frac{5^3\times 4^2{\text{-5}}^2\times 4^3}{5\times 4}=20$