Use the product of powers property to simplify the expression –2x3y4x2y3.

–2(xy)12

–2(xy)72

–2x6y12

–2x5y7

Option d: is the correct answer.

Explanation:

The expression is

We need to simplify the expression, using the product of powers.

The product of powers states that "when multiplying two powers with the same base the exponent values can be added up".

Thus, grouping the same base and adding the exponent values from the expression , we have,

Adding the exponent, we get,

Thus, the simplified expression is

Hence, Option d is the correct answer.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.