Question

Which expression is equivalent to(3m^-2 n)^-3/6mn^-2? Assume

Answer 1

To simplify the expression (3m⁻² n)⁻³/6mn⁻², follow the steps: apply the negative exponent rule, simplify by multiplying the exponents, and rearrange and combine like terms if necessary.

Step-by-step explanation:

To simplify the expression (3m-2 n)-3/6mn-2 , let's break it down step by step:

Step 1: Apply the negative exponent rule. To do this, we can move any term with a negative exponent from the numerator to the denominator or vice versa. In this case, the term m-2 can be written as 1/m2.

Step 2: Simplify the expression by multiplying the exponents. The exponents in the expression can be added since they have the same base (m).

Step 3: Simplify further by rearranging and combining like terms if necessary.

Putting it all together, the expression is equivalent to (1/3m4n6)1/6mn-2.

Answer 2

The formula is:

`((3m^(-2)n)^(-3))/(6mn^(-2))=(1)/(3m^(-2)n)\cdot(1)/(6mn^(-2))\\ =(m^2)/(3n)\cdot(n^2)/(6m)\\ =(n^2)/(3n)\cdot(m^2)/(6m)\\ =(n)/(3)\cdot(m)/(6)\\ =(nm)/(18).`
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