Question

Simplify the expression (m⁻⁴/3m⁻⁶)⁻³ and write your answer using only positive exponents.

Answer 1

To simplify the expression (m⁻⁴/3m⁻⁶)⁻³ and write the answer using only positive exponents, we need to apply the power of a power rule and simplify step by step to get 1/(27m⁶).

Step-by-step explanation:

To simplify the expression (m⁻⁴/3m⁻⁶)⁻³ and write the answer using only positive exponents, we need to apply the power of a power rule which states that (aⁿ)ᵐ = a^(n*m). Let's simplify step by step:

1. Simplify the expression inside the parentheses: m⁻⁴/3m⁻⁶. We can rewrite this as (1/m⁴) / (3/m⁶).
2. Multiply the denominator by the reciprocal: (1/m⁴) * (m⁶/3).
3. Combine the fractions: m⁶ / (3m⁴).
4. Rewrite the expression with positive exponents: 1/(3m⁻²).
5. Cubing this expression, we raise both the numerator and denominator to the power of 3: (1/(3m⁻²))³ = (1³)/(3³m⁻⁶).
6. Simplify the expression: 1/27m⁻⁶.
7. Finally, rewrite the expression with positive exponents: 1/(27m⁶).