Final answer:
To simplify the expression, apply the exponent to both the coefficient and variables inside the parentheses and correctly use the basic exponent rules. Negative exponents denote a division, and scientific notation may require adjustment of exponents when converting between forms.
Step-by-step explanation:
Exponent Rules in Algebra
To simplify the expression (8x⁴y(−9))²/(3), we must apply the exponent rules correctly. The operation within the parentheses should be performed first. We know that when we have negative numbers or variables inside and raise the entire expression to a power, we must apply that power to both the coefficient and variables. Moreover, any number raised to an exponent should follow basic exponent rules such as x¹⁶ = x⁴ · x¹² = x⁴⁶.
The proper power affects everything inside the parentheses. For instance, (27x³)(4x²) = 2.1 × 10³³. Similarly, when multiplying exponentiated quantities, such as 3.2 × 10³ times 2 × 10², we can recognize it as 6.4 × 10⁵.
Negative exponents flip the construction to the denominator, as seen with 1/x⁻⁹, which represents a division. When we work with scientific notation or convert between forms, we adjust the exponent accordingly, for example, 0.183 × 10⁴ becomes 1.83 x 10³.
Converting the exponents to the same value allows for easier subtraction or addition, such as (6.923 × 10⁻³) - (0.8756 × 10⁻³) = (6.923 - 0.8756) × 10⁻³.
The expression given can be simplified as (8x⁴y(-9))²/(3) = (72x⁸y²)/3, which simplifies further to 24x⁸y².