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AlladinOne [14]
3 years ago
11

What is the simplest form of ^3 square root 27a^3b^7

Mathematics
2 answers:
Flura [38]3 years ago
8 0

Answer:

Option (a) is correct.

The simplified form of  \sqrt[3]{27a^3b^7} is 3ab^2\sqrt[3]{b}

Step-by-step explanation:

Given : \sqrt[3]{27a^3b^7}

We have to write the simplest form of given expression \sqrt[3]{27a^3b^7}        

Consider the given expression  \sqrt[3]{27a^3b^7}

27 can be written as 3³

b^7 can be written as b^3b^3b

Thus, expression becomes,

\sqrt[3]{27a^3b^7}=\sqrt[3]{3^3a^3b^6b^3b}

Thus, Simplify, we get,

=3ab^2\sqrt[3]{b}

Thus, The simplified form of  \sqrt[3]{27a^3b^7} is 3ab^2\sqrt[3]{b}

Irina-Kira [14]3 years ago
4 0
\bf \sqrt[3]{27a^3b^7}\quad 
\begin{cases}
27=3\cdot 3\cdot 3\\
\qquad 3^3\\
b^7=b^{3+3+1}\\
\qquad b^3b^3b^1\\
\qquad (b^2)^3b^1
\end{cases}\implies \sqrt[3]{3^3a^3(b^2)^3b^1}
\\\\\\
3ab^2\sqrt[3]{b^1}\implies 3ab^2\sqrt[3]{b}
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System of linear equations.<br> 2x + 4y =, 10<br> 2x + 2y + 3z = 3<br> -3x + y + 2z = -3
Dimas [21]

Answer:

x = 1, y = 2, z = -1

Step-by-step explanation:

2x + 4y = 10

2x = -4y + 10

x = -2y + 5

now sub -2y + 5 in for x, back into the other 2 equations

2x + 2y + 3z = 3                                   -3x + y + 2z = -3

2(-2y + 5) + 2y + 3z = 3                       -3(-2y + 5) + y + 2z = -3

-4y + 10 + 2y + 3z = 3                           6y - 15 + y + 2z = -3

-2y + 3z = 3 - 10                                    7y + 2z = - 3 + 15

-2y + 3z = - 7                                         7y + 2z = 12

-2y + 3z = -7....multiply by 2

7y + 2z = 12...multiply by -3

--------------------------

-4y + 6z = -14 (result of multiplying by 2)

-21y - 6z = -36 (result of multiplying by -3)

---------------------------add

-25y = - 50

y = -50/-25

y = 2 <===

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2x + 4(2) = 10                      2(1) + 2(2) + 3z = 3

2x + 8 = 10                          2 + 4 + 3z = 3

2x = 10 - 8                            6 + 3z = 3

2x = 2                                   3z = 3 - 6

x = 2/2                                 3z = -3

x = 1  <==                              z = -3/3

                                            z = -1 <===

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