Question

Simplify the following expression if possible. Use only positive exponents in your answer and reduce all coefficients: 15x^2/10x^6

Answer 1

To simplify 15x^2/10x^6, divide the coefficients and subtract the exponents, giving 1.5/x^(-4), and then multiply the numerator and denominator by 2 to remove the decimal, resulting in the simplified form 3/x^4 with only positive exponents.

Step-by-step explanation:

To simplify the expression 15x^2/10x^6, we can follow the rules for Division of Exponentials. First, divide the coefficient (digit term) of the numerator by the coefficient of the denominator:

15 ÷ 10 = 1.5

Now we subtract the exponents of the variables. When dividing exponential terms with the same base, subtract the exponent in the denominator from the exponent in the numerator:

x^2 ÷ x^6 = x^(2-6) = x^(-4)

Since we want only positive exponents, we can take the reciprocal of x^(-4) to make the exponent positive:

x^(-4) = 1/x^4

Combining the coefficient with the variable, we have:

1.5/x^4

However, to ensure all coefficients are reduced and no fraction remains, we multiply both the numerator and the denominator by 2 to remove the decimal:

(1.5 × 2)/(x^4 × 2) = 3/x^4