IDNLearn.com: Your trusted platform for finding reliable answers. Join our community to receive prompt and reliable responses to your questions from experienced professionals.
Sagot :
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]
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]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.