Question

Need help please with step by step

Answer 1

Recall some properites of exponentiation:

`a^b* a^c=a^(b+c)`

`\left(a^b\right)^c=a^(b* c)`

So for

(-2 x ² y ⁻¹) ⁻² (5 x ³ y) ²

first distribute the outermost exponents across each product:

((-2)⁻² (x ²)⁻² (y ⁻¹)⁻²) (5² (x ³)² y ²)

Simplify the powers using the multiplication property (the second one listed above) of exponents:

((-2)⁻² x ⁻⁴ y ²) (5² x ⁶ y ²)

Combine powers of the same terms using the addition property (the first one):

(-2)⁻² 5² x ⁻⁴⁺⁶ y ²⁺²

(-2)⁻² 5² x ² y ⁴

Finally, simplify the coefficient:

(-2)⁻² = 1 / (-2)² = 1/4

5² = 25

So you end up with

25/4 x ² y ⁴