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To solve the expression \( \frac{2^{10}}{2^4} \) using indices:

### Step 1: Apply the Laws of Exponents
We can simplify the expression by using the quotient rule of exponents, which states:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, \( a = 2 \), \( m = 10 \), and \( n = 4 \).

### Step 2: Subtract the Exponents
\[
\frac{2^{10}}{2^4} = 2^{10-4} = 2^6
\]

Thus, the simplified expression using indices is:
\[
2^6
\]

Would you like any further clarification on this solution?

### Related Questions:
1. How would you simplify \( \frac{3^7}{3^2} \) using indices?
2. What happens when you divide powers with the same base but the exponents are equal?
3. How can you express \( \frac{5^{12}}{5^7} \) using indices?
4. How do you simplify \( \frac{10^8}{10^3} \) using the laws of exponents?
5. What is the general formula for dividing exponents with the same base?

### Tip:
Remember, when dividing powers with the same base, subtract the exponents to simplify the expression.

Simplify the expression \( \frac{2^{10}}{2^4} \) using indices.

Learn how to simplify the expression \( \frac{2^{10}}{2^4} \) using indices. This problem demonstrates the use of the quotient rule of exponents, where the exponents are subtracted when dividing powers with the same base. Suitable for students in Grades 7-9.

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