Question

Which expression is equivalent to 3x⁻⁶y⁻³/ 15x²y¹⁰? Assume x ≠0,y≠0?

a. 5/x¹²y³⁰
b. 1/5x⁸y¹³
c. 5/x⁴y⁷
d. y⁷/5x⁴

Answer 1

The equivalent expression to 3x⁻⁶y⁻³ divided by 15x²y¹⁰ is 1/5x⁻⁻⁻⁴y⁻¹³, which simplifies the original expression using the rules of exponents.

Step-by-step explanation:

The expression which is equivalent to 3x⁻⁶y⁻³ divided by 15x²y¹⁰ can be found by simplifying the fraction. Here are the steps for simplification:

1. First, divide the coefficients (3/15) which simplifies to 1/5.
2. Next, subtract the exponents of x in the numerator from the exponents of x in the denominator (-6 - 2 = -8), giving x⁻⁻⁻⁴.
3. Then, subtract the exponents of y in the numerator from the exponents of y in the denominator (-3 - 10 = -13), resulting in y⁻¹³.

Therefore, the simplified form of the expression is 1/5x⁻⁻⁻⁴y⁻¹³. Option (b) is equivalent.