Simplify the product using the rules for exponents. (4^2)^4

Mathematics

2 answers:

galben [10]3 years ago

8 0

$(4^2)^4 = 4^{ (2 \times 4)} = 4^8 = 65536$

elixir [45]3 years ago

4 0

<h3>Answer ↓</h3>

$\Large\text{65,536}$

<h3>Calculations ↓</h3>

In order to simplify this expression , we have to multiply the powers (notice that we have <em>a power to a power</em>)

Simplify as follows :

(4²)⁴ = 4⁽²ˣ⁴)=4⁸

4 times itself 8 times simplifies to :

$\footnotesize\text{hope\:helpful~}$

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Which of the following descriptions represent the transformation shown in the image? Part 3b<br>

Igoryamba

Answer: d) none of the above

<u>Step-by-step explanation:</u>

Start at Black Triangle: B = (0, -4) C = (4, -1) D = (2, -5)

End up at Red Triangle: B = (2, 0) C = (-2, 3) D = (0, -1)

Rotation of 180°: (x, y) → (-x, -y)

Reflection across y-axis: (x, y) → ( -x, y)

Reflection across x-axis: (x, y) → (x, -y)

Reflection across x=1: (x, y) → (2 - x, y)

$a) \\\begin{array}{ccc}\qquad \text{(x, y)}&\text{Rotate 180}^o&\text{reflect across y-axis}\\B:\ (0, -4)&(0, 4)&(0,4)\\C: (4, -1)&(-4,1)&(4,1)\\D: (2, -5)&(-2,5)&(2,5)\end{array}$

$b) \\\begin{array}{ccc}\qquad \text{(x, y)}&\text{Rotate 180}^o&\text{reflect across x = 1}\\B:\ (0, -4)&(0, 4)&(2,4)\\C: (4, -1)&(-4,1)&(6,1)\\D: (2, -5)&(-2,5)&(4,5)\end{array}$

$c) \\\begin{array}{ccc}\qquad \text{(x, y)}&\text{Rotate 180}^o&\text{reflect across x-axis}\\B:\ (0, -4)&(0, 4)&(0,-4)\\C: (4, -1)&(-4,1)&(-4,-1)\\D: (2, -5)&(-2,5)&(-2,-5)\end{array}$