Question

Simplify ((2)/(3)a⁻⁴b⁷)⁻³. write the expression with positive exponents.

Answer 1

The expression ((2)/(3)a⁻⁴b⁷)⁻³ simplifies to 27/8 a¹² b¹²¹ when written with positive exponents.

Step-by-step explanation:

To simplify the expression ((2)/(3)a⁻⁴b⁷)⁻³ and write it with positive exponents, we apply the rule that when we raise an expression inside parentheses to a power, the power affects everything inside the parentheses. Given that the negative exponent means we take the reciprocal of the base and then apply the positive exponent, we would first reciprocate the given fraction and then cube each term inside the parentheses.

Here are the steps:

1. Take the reciprocal of the fraction, which gives us: (3/2) a⁴ b⁻⁷
2. Cube the digit term in the usual way and cube the coefficients, which results in: 27/8
3. Multiply the exponent of the exponential term by 3, to get: a¹² b⁻²¹

The final simplified expression with positive exponents is: 27/8 a¹² b¹²¹.