How do you simplify (2^3)^2?

To simplify \((2^3)^2\), you multiply the exponents to get \(2^{3 \times 2} = 2^6\).

When you have a power raised to another power, you can simplify it by multiplying the exponents. In this case, \((2^3)^2\) means you have \(2^3\) raised to the power of 2. According to the laws of indices (or exponents), specifically the power of a power rule, you multiply the exponents together. So, you calculate \(3 \times 2\), which equals 6. Therefore, \((2^3)^2\) simplifies to \(2^6\).

To break it down further, \(2^3\) means \(2 \times 2 \times 2\), which equals 8. When you raise 8 to the power of 2, you get \(8 \times 8\), which equals 64. Alternatively, using the simplified form \(2^6\), you calculate \(2 \times 2 \times 2 \times 2 \times 2 \times 2\), which also equals 64. Both methods give you the same result, confirming that \((2^3)^2\) simplifies correctly to \(2^6\).