Question

Write 9b^2c^2 and 100m^2n^6 as squares of a monomial.
plz help
Write –a^3b^6 and –27x^6b^9 as cubes of a monomial.

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also this one if u can (if u get it wrong i'll still mark u brainliest : ))
1/5b^3 (Find the volume of a cube with the given side length.)

ILL MARK BRAINLIEST JUST PLEASE HELP

Answer 1

Answer:

1. (3bc)^2

2. (10mn^3)^2

3.

   b^9

   -------      ( as a fraction the top number is b^9 and the bottom is 125)

   125  

Step-by-step explanation:

its hard to explain sorry but if you really want to know just comment and ill provide another answer sorry again. but i can explain the last one, so to find the cube you have to multiply that one side by the power of three, so if it was 4, you would do 4^3, but since its 1/5b^3, it would be (1/5b^3)^3

hope this rlly helps

:)

Answer 2

A monomial is an expression that has a single term.

(a) 9b^2c^2 and 100m^2n^6

We have:

$\mathbf{9b^2c^2}$

Express 9 as 3^2

$\mathbf{9b^2c^2 = 3^2b^2c^2}$

Factor out the squares

$\mathbf{9b^2c^2 = (3bc)^2}$

Similarly;

$\mathbf{100m^2n^6}$

Express 100 as 10^2 and n^6 as n^3^2

$\mathbf{100m^2n^6 = 10^2m^2(n^3)^2}$

Factor out the squares

$\mathbf{100m^2n^6 = (10mn^3)^2}$

Hence, 9b^2c^2 and 100m^2n^6 as squares are: $\mathbf{(3bc)^2}$ and $\mathbf{(10mn^3)^2}$

(b) -a^3b^6 and -27x^6b^9

We have:

$\mathbf{-a^3b^6}$

Express b^6 as b^2^3

$\mathbf{-a^3b^6 = -a^3(b^2)^3}$

Factor out the cubes

$\mathbf{-a^3b^6 = (-ab^2)^3}$

Similarly;

$\mathbf{-27x^6b^9}$

Express -27 as -3^3, x^6 as x^2^3 and b^9 as b^3^3

$\mathbf{-27x^6b^9 = (-3)^3(x^2)^3(b^3)^3}$

Factor out the cubes

$\mathbf{-27x^6b^9 = (-3x^2b^3)^3}$

Hence,  –a^3b^6 and –27x^6b^9 as cubes are: $\mathbf{ (-ab^2)^3}$ and $\mathbf{(-3x^2b^3)^3}$

(c) Side length of a cube

The volume is given as:

$\mathbf{Volume=\frac15b^3}$

Take cube roots of both sides

$\mathbf{\sqrt[3]{Volume}= \sqrt[3]{\frac15b^3}}}$

This gives

$\mathbf{\sqrt[3]{Volume}= b\sqrt[3]{\frac15}}}$

So, we have:

$\mathbf{Length= b\sqrt[3]{\frac15}}}$

Hence, the length of the cube is $\mathbf{b\sqrt[3]{\frac15}}}$

Read more about monomials at:

https://brainly.com/question/11363511