Question

Simplify the given expression. Write your answer with positive exponents.

(ma⁶)² * 1/m⁵a²

Answer 1

To simplify the expression (ma⁶)² * 1/m⁵a², we square the contents of the first set of parentheses, multiply the following expressions, and then combine and adjust the exponents to ensure they are all positive. The simplified expression with positive exponents is 1/m³a¹⁴.

Step-by-step explanation:

To simplify the expression (ma⁶)² * 1/m⁵a² with positive exponents, we perform the following steps:

1. Apply the power of 2 to each element inside the first parentheses: (m²)(a⁶)² = m²a¹²
2. Multiply the simplified expression by the second expression: m²a¹² * 1/m⁵a²
3. Combine the exponents for m and a: m² * m⁻⁵ * a¹² * a² = m⁻³ * a¹⁴
4. Since the instructions require positive exponents, write m with a positive exponent by taking its reciprocal: m⁻³ = 1/m³
5. The expression with positive exponents is: 1/m³a¹⁴