Certainly! Let's simplify the given expression step-by-step.
Given expression:
[tex]\[
\frac{5 x^3 \times (2 x)^2}{20 x^4}
\][/tex]
### Step 1: Simplify the numerator
First, we need to simplify the numerator: [tex]\(5 x^3 \times (2 x)^2 \)[/tex].
1. Calculate [tex]\((2 x)^2\)[/tex]:
[tex]\[
(2 x)^2 = 2^2 \times x^2 = 4 x^2
\][/tex]
2. Substitute this back into the numerator:
[tex]\[
5 x^3 \times 4 x^2
\][/tex]
3. Multiply the constants and combine the exponents of [tex]\(x\)[/tex]:
[tex]\[
5 \times 4 \times x^{3+2} = 20 x^5
\][/tex]
So, the simplified numerator is [tex]\(20 x^5\)[/tex].
### Step 2: Simplify the denominator
The denominator is already in its simplified form:
[tex]\[
20 x^4
\][/tex]
### Step 3: Simplify the entire fraction
Now we have the fraction:
[tex]\[
\frac{20 x^5}{20 x^4}
\][/tex]
1. Cancel out the common factor of 20 in the numerator and the denominator:
[tex]\[
\frac{20 x^5}{20 x^4} = \frac{x^5}{x^4}
\][/tex]
2. Simplify the exponents of [tex]\(x\)[/tex] by subtracting the exponent in the denominator from the exponent in the numerator:
[tex]\[
\frac{x^5}{x^4} = x^{5-4} = x^1 = x
\][/tex]
Thus, the simplified form of the given expression is:
[tex]\[
x
\][/tex]
So, [tex]\(\frac{5 x^3 \times (2 x)^2}{20 x^4} = x\)[/tex].
