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3 years ago

If 101! = (99!)x, then x = ?

Mathematics

1 answer:

beks73 [17]3 years ago

5 0

$99!x=101!\ \ \ /:99!\\\\x=\frac{101!}{99!}\\\\x=\frac{99!\cdot100\cdot101}{99!}\\\\x=100\cdot101\\\\x=10\ 100$

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Can anyone help me!

zhenek [66]

Answer:

$\large \text{$ \sf 2^{-64}$}$

Step-by-step explanation:

Given:

$\large \text{$ \sf (256)^{-4^{\frac{3}{2}}}$}$

This reads as: 256 to the power of "-4 to the power of 3/2".

Therefore, we need to deal with the "-4 to the power of 3/2" first.

Rewrite the 4 as 2²:

$\large \text{$ \sf \implies -(2^2)^{\frac{3}{2}}$}$

$\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:$

$\large \text{$ \sf \implies -2^{\left(2 \times \frac{3}{2}\right)}$}$

$\large \text{$ \sf \implies -2^{3}$}$

Therefore:

$\large \text{$ \sf \implies -2^3=(-2)(-2)(-2) = -8$}$

Replace "-4 to the power of 3/2" with -8 :

$\large \text{$ \sf \implies 256^{-8}$}$

Rewrite 256 as 2⁸ :

$\large \text{$ \sf \implies (2^8)^{-8}$}$

$\textsf{Again, apply exponent rule} \quad (a^b)^c=a^{bc}:$

$\large \text{$ \sf \implies 2^{(8 \times -8)}$}$

$\large \text{$ \sf \implies 2^{-64}$}$

In one complete calculation:

$\large\begin{aligned} \sf (256)^{-4^{\frac{3}{2}}} & = \sf (256)^{-(2^2)^{\frac{3}{2}}}\\& = \sf (256)^{-2^{\left(2 \times \frac{3}{2}\right)}}\\& =\sf (256)^{-2^{3}}\\& = \sf (256)^{-8}\\& \sf = (2^8)^{-8}\\& = \sf 2^{(8 \times -8)}\\& =\sf 2^{-64}\end{aligned}$

Learn more about exponent rules here:

brainly.com/question/28211147

brainly.com/question/27959936

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1 year ago

Read 2 more answers

Write the two consecutive integers between which the given rational lies

meriva

Answer:

a) -1, 0

b) -5, -4

c) 2, 3

d) -8, -7

Step-by-step explanation:

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2 years ago

Please help I don't undestand

Alla [95]

By applying the law of sines and some algebraic handling, the length of the side LJ is approximately equal to 3.517 units. (Right choice: D)

<h3>What is the missing side of the triangle according to the law of sines?</h3>

The law of sines presents a relationship between sides and <em>opposite</em> angles, which is described below:

9/sin 89° = LJ/sin 23° (1)

LJ = 9 × sin 23°/sin 89°

LJ ≈ 3.517

By applying the law of sines and some algebraic handling, the length of the side LJ is approximately equal to 3.517 units. (Right choice: D)

To learn more on law of sines: brainly.com/question/21634338

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Svetlanka [38]

She counts both piles.

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2 years ago

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Answer:

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Step-by-step explanation:

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