Final answer:
To simplify an expression with exponents, multiply coefficients and add exponents for like bases. An example is (27x3)(4x2), which simplifies to a single exponential term by applying these rules. Remember that powers are multiplied when an entire expression is raised to a power, like in (53)4 becoming 512.
Step-by-step explanation:
To simplify an expression using the laws of exponents, we should recall certain rules that apply when we are dealing with powers. When an expression within parentheses is raised to a power, the exponent applies to each component within the parentheses. For example, simplifying (27x3)(4x2) involves multiplying the coefficients (numbers) and the variables separately.
The coefficients 27 and 4 are multiplied directly, and this is where our numeracy skills come into play. When we deal with the variables, we add the exponents, according to the division and multiplication of exponentials laws. For instance, x3 multiplied by x2 results in x3+2, which is x5. This illustration shows us that powers are added when multiplying like bases.
A practical example for understanding this concept is looking at (53)4, which can be written as 53×4 or 512. These rules can be extended further when considering more complex operations like series expansions, such as the Binomial theorem, where exponents play a critical role in determining the coefficients of the expanded terms.