1. **State the problem:** Find an easy way to determine that $1024 = 2^{10}$ without memorizing it. 2. **Recall the concept of powers:** To find $2^{10}$, you multiply 2 by itself 10 times: $2 \times 2 \times \cdots \times 2$ (10 times). 3. **Use repeated multiplication or doubling:** Start from 1 and keep doubling: - $2^1 = 2$ - $2^2 = 4$ - $2^3 = 8$ - $2^4 = 16$ - $2^5 = 32$ - $2^6 = 64$ - $2^7 = 128$ - $2^8 = 256$ - $2^9 = 512$ - $2^{10} = 1024$ 4. **Use logarithms or calculators:** If allowed, use $\\log_{10}$ or $\\log_2$ on a calculator to find the exponent: - Calculate $\\log_2 1024$ which gives 10. 5. **Use factorization:** Break down 1024 into factors of 2: - Divide 1024 by 2 repeatedly until you reach 1. - Count how many times you divided by 2; that count is the exponent. **Final answer:** The easiest way is to repeatedly double starting from 1 or repeatedly divide 1024 by 2 and count the steps to find the exponent 10.