What is the simplified form of the expression k^3(K^7/5)^-5

1 answer:

3 0

$\bf k^3\left( \cfrac{k^7}{5} \right)^{-5}\implies k^3\left( \cfrac{5}{k^7} \right)^5\implies k^3\left( \cfrac{5^5}{k^{7\cdot 5}} \right)\implies k^3\cdot \cfrac{5^5}{k^{35}}
\\\\\\
k^3\cdot 5^5\cdot k^{-35}\implies 5^5\cdot k^{3-35}\implies 5^5k^{-32}\implies \cfrac{5^5}{k^{32}}\implies \cfrac{3125}{k^{32}}$

You might be interested in

If f (n)(0) = (n + 1)! for n = 0, 1, 2, , find the taylor series at a=0 for f.

Pie

Given that $f^{(n)}(0)=(n+1)!$ , we have for $f(x)$ the Taylor series expansion about 0 as

$f(x)=\displaystyle\sum_{n=0}^\infty\frac{(n+1)!}{n!}x^n=\sum_{n=0}^\infty(n+1)x^n$

Replace $n+1$ with $n$ , so that the series is equivalent to

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}$

and notice that

$\displaystyle\frac{\mathrm d}{\mathrm dx}\sum_{n=0}^\infty x^n=\sum_{n=1}^\infty nx^{n-1}$

Recall that for $|x|$ , we have

$\displaystyle\sum_{n=0}^\infty x^n=\frac1{1-x}$

which means

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}=\frac{\mathrm d}{\mathrm dx}\frac1{1-x}$
$\implies f(x)=\dfrac1{(1-x)^2}$

5 0

3 years ago

Hey can u please help please

atroni [7]

In a triangular prism, B usually stand for the triangular base of the prism. It is the area of the triangle.

Area of a right triangle = ab/2
a = long leg ; b = short leg

Given measures are:
a = 4 yd ; b = 3 yd

A = (4 yd * 3 yd)/2 = 12 yd² / 2 = 6 yd² is the value of B.

the hypotenuse is 5 yd but it is not needed to get the area of the right triangle base. 7 yd is the measure of the height of the triangular prism.

5 0

3 years ago

Read 2 more answers

The area of the trapezoid is 9 square centimeters.

Lana71 [14]

Answer:

Height : 3 cm

Step-by-step explanation:

The formula for a trapezoid is

<u> a+b</u> ×height

Rearrange for formula :

$2 \times \frac{area}{ base + base }$