How do you calculate (3^2 * 3^4)?

To calculate \((3^2 \times 3^4)\), you add the exponents to get \(3^{2+4} = 3^6\).

When multiplying numbers with the same base, you can simplify the expression by adding the exponents. This is because of the laws of indices (or exponents). In this case, both terms have the base 3. The first term is \(3^2\), which means 3 raised to the power of 2, and the second term is \(3^4\), which means 3 raised to the power of 4.

According to the rule for multiplying powers with the same base, you add the exponents together. So, you take the exponent from \(3^2\) (which is 2) and the exponent from \(3^4\) (which is 4) and add them together: \(2 + 4 = 6\). This gives you \(3^6\).

To understand why this works, consider what each term represents. \(3^2\) is \(3 \times 3\), and \(3^4\) is \(3 \times 3 \times 3 \times 3\). When you multiply these together, you have \(3 \times 3 \times 3 \times 3 \times 3 \times 3\), which is six 3s multiplied together, or \(3^6\).

So, \((3^2 \times 3^4)\) simplifies to \(3^6\), which is a much more manageable form. If you need the numerical value, you can then calculate \(3^6\) as \(3 \times 3 \times 3 \times 3 \times 3 \times 3 = 729\).