Explanation

Given the expression:

[(2/13)⁶ + (2/13)³]³ × (2/13)^-⁹

Let's simplify:

= [(2/13)³((2/13)³ + 1)]³ × (2/13)^-⁹

= (2/13)⁹[(2/13)³ + 1]³ × (2/13)^-⁹

The (2/13)⁹ and (2/13)^-⁹ cancel out:

= [(2/13)³ + 1]³

Given the result is 1, let's assume:

[(2/13)³ + 1]³ = 1

Explanation

Let's simplify the equation:

(-16k) + (-k) - 15k - (-11k) - (-17k) = 1

Combine like terms:

-16k - k - 15k + 11k + 17k = 1

-4k = 1

Divide by -4:

k = -1/4

Explanation

(1+2⁰+3²+4⁰) / (5+6⁰):

(1 + 1 + 9 + 1) / (5 + 1)

= 12 / 6

= 2

Explanation

1 + tan²θ = Sec²θ

This is a fundamental trigonometric identity.

Explanation

The phrase "delighted with" is correctly used to express pleasure or satisfaction about something.

So, "delighted with the generosity" is grammatically and idiomatically correct.

Explanation

The correct phrase is "associated with", meaning connected or linked to something.

So, "associated with agriculture" correctly shows the relationship between village life and farming.

Explanation

The correct phrase is "Let such in peace depart".

It often used in formal or poetic expressions like prayers or blessings.

It means to allow someone or something to leave peacefully or in a state of peace.

Explanation

"Along the coast" means following the line of the shore, which suits marine fishing.

It's the correct preposition when referring to activities happening beside or near a coastline.

Explanation

The correct phrase is "beg forgiveness of someone", meaning to ask that person for pardon.

So, "beg forgiveness of this gentleman" is grammatically correct and idiomatic.

Explanation

Conclude means کسی چیز کو ختم کرنے یا ختم کرنے کے لئے

Begin means اسے شروع کرنے کے لئے