Simplify 10⁴/5⁴ and write it in exponential form.

Question 17 of 28beginner🔧 ApplyNumerical2 marks

Simplify $\frac{10^4}{5^4}$ and write it in exponential form.

Correct Answer

Given: $\frac{10^4}{5^4}$

Formula: $\frac{m^a}{n^a} = \left(\frac{m}{n}\right)^a$

Substitution: $\frac{10^4}{5^4} = \left(\frac{10}{5}\right)^4$

Calculation: $\left(\frac{10}{5}\right)^4 = 2^4 = 16$

Answer: $\frac{10^4}{5^4} = \mathbf{2^4} = \mathbf{16}$

Exercise: Magical Pond | Q: 1 | (Page Page 7)

For More Understanding

Explanation

Using the property $\frac{m^a}{n^a} = \left(\frac{m}{n}\right)^a$ , we have $\frac{10^4}{5^4} = \left(\frac{10}{5}\right)^4 = 2^4 = 16$ . The chapter introduces this general form $\frac{m^a}{n^a} = \left(\frac{m}{n}\right)^a$ .

Solution Steps

Step 1: Apply the property $\frac{m^a}{n^a} = \left(\frac{m}{n}\right)^a$
Step 2: $\frac{10^4}{5^4} = \left(\frac{10}{5}\right)^4 = 2^4$
Step 3: $2^4 = 16$

Previous Next