Final answer:
When multiplying powers with the same base, add the exponents together to simplify the expression, such as in 5^3 * 5^4 equals 5^7. In scientific notation, multiply coefficients and add exponents of powers of ten. Remember, these properties only apply when the bases of the exponents are the same.
Step-by-step explanation:
When multiplying powers of the same base, you follow the multiplication properties of exponents. This process involves multiplying the numeric coefficients (if any) normally and then adding the exponents together. For instance, with the expression 53 × 54, you would keep the base of 5 and add the exponents together: 3 + 4 to get 57. The base remains the same because the properties of exponents dictate that when the bases are the same, the powers can be simplified by adding the exponents, resulting in a single exponential expression.
Another example is when multiplying numbers in scientific notation, such as 3.2 × 103 times 2 × 102. You would multiply the digit terms to get 6.4 and then add the exponents to get 105, resulting in the final answer of 6.4 × 105. It's important to note that this property only applies to exponents with the same base; if the bases are different, the exponents cannot be simply added.
Moreover, squaring an exponential term like (xa)2 would result in x2a, as you multiply the exponent by 2.