Simplify the expression.

can anyone explain to me how to do this?

last option 32x⁷y¹⁵ is the correct answer.

Step-by-step explanation:

Identities

1). (xᵃ)ᵇ = xᵃᵇ

2). xᵃxᵇ = x⁽ᵃ⁺ ᵇ)

To find the value of expression

The given expression is,

(x²)(2xy³)⁵

Using the above identities we can evaluate the value of expression

⇒ (x²)*(2)⁵ *(x)⁵ * (y³)⁵

⇒ (2)⁵ * (x²) *(x)⁵ *(y³)⁵

⇒  32* (x²⁺⁵) *(y³ˣ⁵)

⇒  32 * x⁷ *y¹⁵

⇒  32x⁷y¹⁵

Therefore last option 32x⁷y¹⁵ is the correct answer.

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.