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2 years ago

Simplify (2m^6)^3.

Mathematics

2 answers:

labwork [276]2 years ago

8 0

Answer:

B. 8m ^ 18

Step-by-step explanation:

(2m ^6)^3 is the same as ;

(2 ^1 × m ^ 6) ^ 3.....multiply the powers 1 and 6 by 3

2 ^ (1×3) × m ^ (6×3).....this equals;

2 ^ 3 × m ^ 18

8m^18

hope this helps :)

Sophie [7]2 years ago

5 0

<u>B. 8m^18</u>

Answer:

Solution given:

$(2m^6)^3$

since cube is of all

distribute it

$2³(m^6)^3$

we have

2³=8

and

power is multiplied to its power

$m^{6*3}$

$m^{18}$

and

we finally get

$\bold{8m^{18}}$

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Find the answer to the question please 16t^4/8t

sammy [17]

Answer:

STEP

Equation at the end of step 1

((16 • (t4)) - 23t2) + 1

STEP

Equation at the end of step

(24t4 - 23t2) + 1

STEP

Trying to factor by splitting the middle term

3.1 Factoring 16t4-8t2+1

The first term is, 16t4 its coefficient is 16 .

The middle term is, -8t2 its coefficient is -8 .

The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 16 • 1 = 16

Step-2 : Find two factors of 16 whose sum equals the coefficient of the middle term, which is -8 .

-16 + -1 = -17

-8 + -2 = -10

-4 + -4 = -8 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and -4

16t4 - 4t2 - 4t2 - 1

Step-4 : Add up the first 2 terms, pulling out like factors :

4t2 • (4t2-1)

Add up the last 2 terms, pulling out common factors :

1 • (4t2-1)

Step-5 : Add up the four terms of step 4 :

(4t2-1) • (4t2-1)

Which is the desired factorization

Trying to factor as a Difference of Squares:

3.2 Factoring: 4t2-1

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 4 is the square of 2

Check : 1 is the square of 1

Check : t2 is the square of t1

Factorization is : (2t + 1) • (2t - 1)

Trying to factor as a Difference of Squares:

3.3 Factoring: 4t2 - 1

Check : 4 is the square of 2

Check : 1 is the square of 1

Check : t2 is the square of t1

Factorization is : (2t + 1) • (2t - 1)

Multiplying Exponential Expressions:

3.4 Multiply (2t + 1) by (2t + 1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (2t+1) and the exponents are :

1 , as (2t+1) is the same number as (2t+1)1

and 1 , as (2t+1) is the same number as (2t+1)1

The product is therefore, (2t+1)(1+1) = (2t+1)2

Multiplying Exponential Expressions:

3.5 Multiply (2t-1) by (2t-1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (2t-1) and the exponents are :

1 , as (2t-1) is the same number as (2t-1)1

and 1 , as (2t-1) is the same number as (2t-1)1

The product is therefore, (2t-1)(1+1) = (2t-1)2

Final result :

(2t + 1)2 • (2t - 1)2

Step-by-step explanation:

4 0

3 years ago

General admission to The American Museum of Natural History is $19.

Reil [10]

Answer:

(a) $2,375.

(b) $2,875.

Step-by-step explanation:

We have been general admission to The American Museum of Natural History is $19.

(a). To find the total cost of tickets for a group of 125 students, we will multiply 125 by $19.

$\text{The total cost of tickets}=\$19\times 125$

$\text{The total cost of tickets}=\$2,375$

Therefore, the total cost of 125 tickets would be $2,375.

(b). We have been given that the group also purchases IMAX movie tickets for an additional $4 per student.

The total cost of one ticket would be the cost of museum ticket plus movie ticket that is $\$19+\$4=\$23$ .

The new total cost of 125 tickets would be 125 times $23.

$\text{The new total cost of tickets}=\$23\times 125$

$\text{The new total cost of tickets}=\$2,875$

Therefore, the new total cost of 125 tickets would be $2,875.

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3 years ago

What is 35 divided by 300

3241004551 [841]

Answer

8.57142857143

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3 years ago

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Please help!!!!!!!!! in the similarity transformation of abc to def, abc was dilated by a scale factor of ?, reflected across th

shusha [124]

The complete similarity transformation is: triangle abc was dilated by a scale factor of [2], reflected across the [x-axis], and moved through the translation [0].

<h3><u>What is Similarity?</u></h3>

When it comes to Euclidean geometry, two things are said to be comparable if they have the same shape or the same shape as each other's mirror image.
More specifically, by uniformly scaling (enlarging or decreasing), maybe with additional translation, rotation, and reflection, one can be created from the other.
This indicates that one object may be properly aligned with the other object by rescaling, moving, and reflecting it. When two things are comparable to one another, one is consistent with the outcome of a specific uniform scaling of the other.

From the figure, we have:

AB = 2 units

DE = 4 units

So, the scale factor (k) is:

k = DE/AB

k = 4/2

k = 2

Also, both shapes are on either sides of the x-axis, and they are equidistant from the x-axis.

This means that the triangle is reflected across the x-axis with no translation.

Hence, the complete similarity transformation is: abc was dilated by a scale factor of [2], reflected across the [x-axis], and moved through the translation [0].

So, the scale factor is 2

Know more about Similarity with the help of the given link:
brainly.com/question/12670209

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5 0

2 years ago

What is the result of subtracting a number greater than -3 but less than -2 from a number greater than 1 and less than 6

leva [86]

Answer:

2/2 - 4 = -3

Step-by-step explanation:

I don't know really but, hopefully this helps. Are there any answer choices?

5 0

2 years ago