Sure! Let's break down the given expression step-by-step to simplify it.
The given expression is:
[tex]\[ \frac{25 \times 5^2 \times x^8}{10^3 \times x^5} \][/tex]
Step 1: Simplify the constants and bases separately.
### Numerator:
[tex]\[ 25 \times 5^2 \times x^8 \][/tex]
Calculate the numerical parts:
[tex]\[ 5^2 = 25 \][/tex]
Thus, the numerator becomes:
[tex]\[ 25 \times 25 \times x^8 = 625 \times x^8 \][/tex]
### Denominator:
[tex]\[ 10^3 \times x^5 \][/tex]
Calculate the numerical part:
[tex]\[ 10^3 = 1000 \][/tex]
Thus, the denominator becomes:
[tex]\[ 1000 \times x^5 \][/tex]
Step 2: Combine the simplified numerator and denominator into the fraction:
[tex]\[ \frac{625 \times x^8}{1000 \times x^5} \][/tex]
Step 3: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor. First, simplify the numerical part:
[tex]\[ \frac{625}{1000} = 0.625 \][/tex]
Step 4: Simplify the variable part [tex]\( \frac{x^8}{x^5} \)[/tex] by using the properties of exponents:
[tex]\[ x^8 \div x^5 = x^{8-5} = x^3 \][/tex]
Step 5: Combine the simplified numerical part and the simplified variable part:
[tex]\[ 0.625 \times x^3 \][/tex]
Thus, the simplified form is:
[tex]\[ \frac{25 \times 5^2 \times x^8}{10^3 \times x^5} = 0.625 \times x^3 \][/tex]
So, the final answer is:
[tex]\[ 0.625x^3 \][/tex]
