Final answer:
The multiplication of exponents with the same base involves adding the exponents. For example, 'x times x^2' is x^3 because the operation is equivalent to x raised to the power of 1+2. Understanding and applying exponent rules simplifies the operations.
Step-by-step explanation:
The question seems to be concerned with the multiplication of powers with the same base. In mathematics, when you multiply two exponents with the same base, you simply add the exponents. For instance, x times x2 would result in x1+2 or x3. This is because exponentiation is a shorthand for repeated multiplication. So x multiplied by x2 is the same as x multiplied by itself twice, which gives us x3. Similarly, if you consider an example such as 51 times 52, this would result in 51+2 or 53.
If we have an expression like (2x)2 equals 4.0 times (1 - x)2, we can take the square root of both sides to simplify. This illustrates that when dealing with equations involving exponents, it's often helpful to use the properties of exponents, such as the power of a product rule or the power of a power rule, as seen with the example (53)4 equals 512.