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Finger [1]
3 years ago
15

Which is equivalent to 64 Superscript one-fourth?

Mathematics
2 answers:
vazorg [7]3 years ago
9 0

Answer:

Option 1 - 64^{\frac{1}{4}}=2\sqrt[4]{4}

Step-by-step explanation:

Given : Expression 64 Superscript one-fourth i.e. 64^{\frac{1}{4}}

To find : Which is equivalent to expression ?

Solution :

Step 1 - Write the expression,

64^{\frac{1}{4}}

Step 2 - Factor the term 64,

=(2\times 2\times 2\times 2\times 2\times 2)^{\frac{1}{4}}

=(2^6)^{\frac{1}{4}}

=(2^4\cdot 2^2)^{\frac{1}{4}}

Step 3 - Apply exponent rule, (x^a)^{\frac{1}{b}}=x^{\frac{a}{b}}

=(2)^{\frac{4}{4}}\cdot (2)^{\frac{2}{4}}

=(2)^{1}\cdot (2)^{\frac{2}{4}}

=2\cdot 4^{\frac{1}{4}}

=2\sqrt[4]{4}

Therefore, 64^{\frac{1}{4}}=2\sqrt[4]{4}

So, Option 1 is correct.

Schach [20]3 years ago
7 0

Answer:

2 RootIndex 4 StartRoot 4 EndRoot

Step-by-step explanation:

we have

64^{\frac{1}{4}}

Decompose the number 64 in prime factors

64=2^{6}=2^{4}2^{2}

substitute

64^{\frac{1}{4}}=(2^{4}2^{2})^{\frac{1}{4}}=2^{\frac{4}{4}}2^{\frac{2}{4}}=2\sqrt[4]{4}

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In the figure, AB is divided into equal parts. The coordinates of point A are (2, 4), and the coordinates of point B are (10, 6)
Rudiy27

Diving the length AB into equal parts gives;

D→\left (4 \:,4.5\right)

E→\left (5 \:,4.75\right)

H→\left (8 \:,5.5\right)

I →\left (9 \:,5.75\right)

<h3>How can the coordinates of the points be found?</h3>

The number of equal parts obtained by counting are 8

Coordinates of point <em>A</em> is (2, 4)

Coordinates of point <em>B </em>is (10, 6)

Therefore;

Coordinates of point <em>C</em> is

\mathbf{ \left (2 + \frac{10 - 2}{8},\:  4 + \frac{6 - 4}{8}\right) }= \left (3 \:, 4.25\right)

Coordinates of point <em>D</em> are;

\mathbf{\left (2 + \frac{10 - 2}{4} \: , 4 + \frac{6 - 4}{4}\right) }= \left (4 \:,4.5\right)

Coordinates of point <em>E</em> are;

\mathbf{\left (2 + \frac{8 \times 3}{8} \: , 4 + \frac{2 \times 3}{8}\right)} = \left (5 \:,4.75\right)

Coordinates of point F are;

\mathbf{\left (2 + \frac{8 \times 4}{8} \: , 4 + \frac{2 \times 4}{8}\right)} = \left (6 \:,5\right)

Coordinates of point <em>H</em> are;

\mathbf{\left (2 + \frac{8 \times 6}{8} \: , 4 + \frac{2 \times 6}{8}\right)} = \left (8 \:,5.5\right)

Coordinates of point <em>I</em> are;

\mathbf{\left (2 + \frac{8 \times 7}{8} \: , 4 + \frac{2 \times 7}{8}\right)} = \left (9 \:,5.75\right)

Which gives;

D→\left (4 \:,4.5\right)

E→\left (5 \:,4.75\right)

H→\left (8 \:,5.5\right)

I →\left (9 \:,5.75\right)

Learn more about distance between points here;

brainly.com/question/10377723

#SPJ1

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