Simplify the expression: \(\frac{5^9 \times 5^{-1}}{5^3}\)
Understand the Problem
The question asks to simplify the expression (\frac{5^9 \times 5^{-1}}{5^3}). This involves using the properties of exponents to simplify the numerator and then dividing by the denominator to arrive at the simplified expression in exponential form.
Answer
$5^5$
Answer for screen readers
$5^5$
Steps to Solve
- Simplify the numerator using the product of powers rule
When multiplying exponential terms with the same base, add the exponents: $5^9 \times 5^{-1} = 5^{9 + (-1)} = 5^{9-1} = 5^8$
- Divide the result by the denominator
When dividing exponential terms with the same base, subtract the exponents: $\frac{5^8}{5^3} = 5^{8 - 3} = 5^5$
$5^5$
More Information
The expression simplifies to $5^5$, which means 5 multiplied by itself 5 times. $5^5 = 5 \times 5 \times 5 \times 5 \times 5 = 3125$.
Tips
A common mistake is to add the exponents in the numerator and denominator instead of subtracting when dividing.
AI-generated content may contain errors. Please verify critical information
