Write 16^8 as a power with a base of 4.

The base of an exponent can be changed from one number to another.

as a power with a base of 4 is

The expression is given as

Where:

base

Express 16 as 4^2

Remove brackets and apply law of indices

Hence;

as a power with a base of 4 is

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4^16

note that 16 = 4²

thus (16)^8 = (4²)^8 = 4^(2 × 8) = 4^16

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this