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1 year ago

Simplify each number. 64²/₃ 64²/₃

Mathematics

1 answer:

Fynjy0 [20]1 year ago

8 0

The result of simplifying each number 64²/₃ 64²/₃ using the exponent rules is 256

To solve this exercise we have to resolve algebraic operations following the exponent rules.

64²/₃ * 64²/₃

Base= 64
Exponent = 2/3

The base number 64 is the same that: 4³, then we get:

(4)³ ⁽²/₃⁾ * (4)³ ⁽²/₃⁾

Using the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:

4⁽³*²/³⁾ * 4⁽³*²/³⁾

4⁽⁶/³⁾ * 4⁽⁶/³⁾

(4)² * (4)²

Using the product rule that indicates that: the exponent result will be the addition of these exponents, we have:

4⁽²⁺²⁾

4⁴

4*4*4*4

256

<h3>What is an exponent?</h3>

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

Learn more about exponent at: brainly.com/question/847241

#SPJ4

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Find the approximate side length of a square game board with an area of 161 in?

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Answer: 12.69 in

Explanation:
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3 years ago

F(x) = x2 + 3x + 2 is shifted 2 units left, the result is g(x). What is g(x)?

Veronika [31]

Answer:

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Step-by-step explanation:

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3 years ago

Find the indicated probabilities using the geometric distribution, Poisson distribution, or the binomial distribution. The mean

ExtremeBDS [4]

Answer:

0.1606 = 16.06% probability that the number of births in any given minute is exactly five.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

In this question:

We only have the mean during an interval, and this is why we use the Poisson distribution.

The mean number of births per minute in a given country in a recent year was about 6.

This means that $\mu = 6$

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This is P(X = 5). So

$P(X = 5) = \frac{e^{-6}*6^{5}}{(5)!} = 0.1606$

0.1606 = 16.06% probability that the number of births in any given minute is exactly five.

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3 years ago

What is the simplified form of the following expression?

ziro4ka [17]

For this case we must simplify the following expression: $7 (\sqrt [3] {2x}) - 3 (\sqrt [3] {16x}) - 3 (\sqrt [3] {8x})$

We rewrite:

$16x = 2 ^ 3 * 2x\\8x = 2 ^ 3 * x$

We rewrite the expression:

$7 (\sqrt [3] {2x}) - 3 (\sqrt [3] {2 ^ 3 * 2x}) - 3 (\sqrt [3] {2 ^ 3 * x}) =$

By definition of properties of powers and roots we have:

$\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}$

Then, taking the terms of the radical:

$7 (\sqrt [3] {2x}) - 3 (2 \sqrt [3] {2x}) - 3 (2 \sqrt [3] {x}) =\\7 \sqrt [3] {2x} -6 \sqrt [3] {2x} -6 \sqrt [3] {x} =$

We add similar terms:

$\sqrt [3] {2x} -6 \sqrt [3] {x}$

Answer:

Option C

7 0

3 years ago