How do you simplify 4^2 * 4^3?

To simplify \(4^2 \times 4^3\), you add the exponents to get \(4^{2+3} = 4^5\).

When you multiply numbers with the same base, you can simplify the expression by adding their exponents. This is because of the laws of indices (or exponents). In this case, both terms have the base 4. The first term is \(4^2\), which means 4 multiplied by itself once (4 * 4). The second term is \(4^3\), which means 4 multiplied by itself twice (4 * 4 * 4).

According to the rule \(a^m \times a^n = a^{m+n}\), where \(a\) is the base and \(m\) and \(n\) are the exponents, you simply add the exponents together. Here, \(m\) is 2 and \(n\) is 3. So, you add 2 and 3 to get 5. Therefore, \(4^2 \times 4^3\) simplifies to \(4^5\).

This rule works because multiplying powers of the same base is essentially combining the number of times you multiply the base by itself. So, \(4^2\) (which is 4 * 4) and \(4^3\) (which is 4 * 4 * 4) together make \(4^5\) (which is 4 * 4 * 4 * 4 * 4). This makes it much easier to handle large numbers and complex expressions.