Identify Operation: Identify the operation needed for the exponents. We need to simplify the expression 5^2(10)^-4. This involves dealing with powers and their exponents.Simplify Using Exponents: Simplify the expression using the properties of exponents. We know that 5^2 means 5 multiplied by itself, which is 25. The expression (10)^-4 means 1 divided by 10^4. So we can rewrite the expression as 25 * 1/10^4.Calculate 10^4: Calculate 10^4. 10^4 means 10 multiplied by itself 4 times, which is 10,000.Combine Results: Combine the results from Step 2 and Step 3. We have 25 * 1/10^4, which is 25/10,000.Simplify Fraction: Simplify the fraction. We can simplify 25/10,000 by dividing both the numerator and the denominator by 25. This gives us 1/400.

Algebra 1

Simplify exponential expressions using exponent rules

Full solution

5^2(10)^{-4}

Identify Operation: Identify the operation needed for the exponents. $\newline$ We need to simplify the expression $5^2(10)^{-4}$ . This involves dealing with powers and their exponents.
Simplify Using Exponents: Simplify the expression using the properties of exponents. $\newline$ We know that $5^2$ means $5$ multiplied by itself, which is $25$ . The expression $(10)^{-4}$ means $1$ divided by $10^4$ . So we can rewrite the expression as $25 \times \frac{1}{10^4}$ .
Calculate $10^4$ : Calculate $10^4$ . $\newline$ $10^4$ means $10$ multiplied by itself $4$ times, which is $10,000$ .
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have $25 \times \frac{1}{10^4}$ , which is $\frac{25}{10,000}.$
Simplify Fraction: Simplify the fraction. $\newline$ We can simplify $\frac{25}{10,000}$ by dividing both the numerator and the denominator by $25$ . This gives us $\frac{1}{400}$ .