Final answer:
The expression 3.6 × 3.6 × 3.6 × 3.6, which is (3.6)⁴, is not equivalent to 3.6 × 4. The first is an exponentiation while the latter is basic multiplication resulting in a larger number for the first expression compared to the second.
Step-by-step explanation:
The expression 3.6 × 3.6 × 3.6 × 3.6 is not equivalent to 3.6 × 4. The former expression represents 3.6 raised to the power of 4, whereas the latter represents just 3.6 multiplied by 4. When calculating the first expression, you have to multiply 3.6 by itself four times. On the other hand, the second expression is a straightforward multiplication which will yield a much smaller product than the first expression.
In terms of exponentiation, the first expression can be written as (3.6)⁴ which signifies 3.6 multiplied by itself four times. Using quick experimentation, one can see that multiplying the base number (3.6) by the number of times it is used as a factor (4 times in this case), gives us a much larger number than just 3.6 multiplied by 4.
Example
If we take a simpler example, such as (2^3)⁴, this would equal 2⁽³ˣ⁴⁾, which is 2¹². This shows how exponents are multiplied when a number raised to a power is itself raised to another power, this is known as the rule of multiplying exponentiated quantities as seen in the context of scientific notation where we multiply powers of 10.