Final answer:
The laws of exponents involve adding or subtracting exponents during multiplication and division when bases are the same. However, for the expressions 4^-3 × 2^-8 and (1/3)x^4, there isn't a direct application of these laws due to different bases.
Step-by-step explanation:
To use laws of exponents to rewrite and simplify the given expressions, it's essential to remember key operations. For multiplication, you add the exponents when the bases are the same, and for division, you subtract the exponents when the bases are the same. Let's simplify the provided examples.
(a) Given the expression 4-3 × 2-8, this cannot be simplified using the laws of exponents directly because the bases are different. Instead, one would need to convert the expression into a form that could be combined or further use algebraic methods to simplify.
(b) The expression 1/3 x4 seems to be missing an operator between the terms. Assuming multiplication is intended, which is often the case in such expressions, the term would stand as it is since no law of exponents applies directly to terms with different bases (1/3 and x).
Division of Exponentials
When dividing expressions with the same base, we utilize the following method: Divide the digits and subtract the exponents. For instance, for 106 / 103, you would subtract the exponents (6-3) to get 103 as the simplified form.