Simplify without negative exponents:

Question

(2m²)^-1/m²

Answer 1

This question tests your understanding of exponent rules. You may find this youtube video helpful (https://www.youtube.com/watch?v=LkhPRz7Hocg)

After reviewing, apply the relevant rules to solve the problem. Particularly the negative exponent rule, treating division as multiplication by the reciprocal, and combining powers of m.

Answer 2

We are asked to simplify the expression:

(2m²)^-1/m²

Step 1: Apply the negative exponent rule

The negative exponent rule states that a⁻ⁿ=1/aⁿ​. Applying this to (2m²)⁻¹

(2m²)^-1=1/(2m²)

So the expression becomes:

1/(2m²)​÷m²

Step 2: Rewrite the division as multiplication

Dividing by m^-2 is the same as multiplying by m⁻²

1/(2m²)​÷m² = 1/(2m²)​*m^-2

Step 3: Combine powers of m

Using the rule m^a⋅m^b=m^(a+b):

1/(2m²)​*m^-2 = m^-2m^-2 /2

So the expression becomes:

m^-2m^-2 /2 = m^-4/2

Step 4: Eliminate the negative exponent

To remove the negative exponent, we use m⁻ⁿ=1/mⁿ

m^-4/2 = 1/(2m⁴)

Answer 3

(2m²)^-1/m² = 2^-1m^-2m^-2 = 2^-1m^-4 = 1/(2m⁴)