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Marysya12 [62]
3 years ago
8

(5^3)^2 . (4^2)^2 . (6^2)^3

Mathematics
1 answer:
Vladimir79 [104]3 years ago
7 0

Answer:

1. 15625

2. 256

3. 46656

Step-by-step explanation:

Simplify the following:

(5^3)^2

Multiply exponents. (5^3)^2 = 5^(3×2):

5^(3×2)

3×2 = 6:

5^6

5^6 = (5^3)^2 = (5×5^2)^2:

(5×5^2)^2

5^2 = 25:

(5×25)^2

5×25 = 125:

125^2

| | 1 | 2 | 5

× | | 1 | 2 | 5

| | 6 | 2 | 5

| 2 | 5 | 0 | 0

1 | 2 | 5 | 0 | 0

1 | 5 | 6 | 2 | 5:

Answer:  15625

_________________________________________

Simplify the following:

(4^2)^2

Multiply exponents. (4^2)^2 = 4^(2×2):

4^(2×2)

2×2 = 4:

4^4

4^4 = (4^2)^2:

(4^2)^2

4^2 = 16:

16^2

| 1 | 6

× | 1 | 6

| 9 | 6

1 | 6 | 0

2 | 5 | 6:

Answer:  256

____________________________________________

Simplify the following:

(6^2)^3

Multiply exponents. (6^2)^3 = 6^(2×3):

6^(2×3)

2×3 = 6:

6^6

6^6 = (6^3)^2 = (6×6^2)^2:

(6×6^2)^2

6^2 = 36:

(6×36)^2

6×36 = 216:

216^2

| | 2 | 1 | 6

× | | 2 | 1 | 6

| 1 | 2 | 9 | 6

| 2 | 1 | 6 | 0

4 | 3 | 2 | 0 | 0

4 | 6 | 6 | 5 | 6:

Answer:  46656

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Add 34+(−212) using the number line. Select the location on the number line to plot the sum.
Korvikt [17]

Answer:

Answer is explained below in the explanation section.

Step-by-step explanation:

Solution:

For this question, we need to have a number line, we can not make the number line here. As it will be very long. Instead, I have attached a number line from -11 to +11 for your understanding and explained it below. Please refer to the attachment below for the number line.

Number Line:

A number line is a line which contains all the numbers from negative infinity to positive infinity divided by a single number zero. It has two sides, left hand side and right hand side. A side left to zero contains all the negative numbers and a side right to 0 contains, all the positive numbers.

So,

We are asked to add 34 in (-212), we will get 178 but with the negative sign, and it will lie on the left hand side of the number line.

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4 0
3 years ago
WILL MARK BRAINLIEST <br><br> what is the domain of (f/g) (x)?
tatyana61 [14]

Given that f(x) = \sqrt{7-x} and g(x) = \sqrt{x + 2}, we can say the following:

\Bigg(\dfrac{f}{g}\Bigg)(x) = \dfrac{f (x)}{g(x)} = \dfrac{\sqrt{7 - x}}{\sqrt{x+2}}


Now, remember what happens if we have a negative square root: it becomes an imaginary number. We don't want this, so we want to make sure whatever is under a square root is greater than 0 (given we are talking about real numbers only).


Thus, let's set what is under both square roots to be greater than 0:

\sqrt{7 - x} \Rightarrow 7 - x \geq 0 \Rightarrow x \leq 7

\sqrt{x + 2} \Rightarrow x + 2 \geq 0 \Rightarrow x \geq -2


Since both of the square roots are in the same function, we want to take the union of the domains of the individual square roots to find the domain of the overall function.

x \leq 7 \,\,\cup x \geq -2 = \boxed{-2 \leq x \leq 7}


Now, let's look back at the function entirely, which is:

\Bigg( \dfrac{f}{g} \Bigg)(x) = \dfrac{\sqrt{7 - x}}{\sqrt{x+2}}

Since \sqrt{x + 2} is on the bottom of the fraction, we must say that \sqrt{x + 2} \neq 0, since the denominator can't equal 0. Thus, we must exclude \sqrt{x + 2} = 0 \Rightarrow x + 2 = 0 \Rightarrow x = -2 from the domain.


Thus, our answer is Choice C, or \boxed{ \{ x | -2 < x \leq 7 \}}.


<em>If you are wondering why the choices begin with the x | symbol, it is because this is a way of representing that x lies within a particular set.</em>

6 0
3 years ago
Fill the value of the expression 24 3/5 +4 ×(8 1/5-2)
Julli [10]
First off, we'll convert the mixed fractions to "improper",

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\bf 24\frac{3}{5}\times \left( 8\frac{1}{5}-2 \right)\implies \cfrac{123}{5}\left( \cfrac{41}{5}-2 \right)\impliedby \mathbb{PEMDAS}&#10;\\\\\\&#10;\cfrac{123}{5}\left( \cfrac{41-10}{5} \right)\implies \cfrac{123}{5}\left( \cfrac{31}{5} \right)&#10;\\\\\\&#10;\cfrac{123\cdot 31}{5\cdot 5}\implies \cfrac{3813}{25}\implies 152\frac{13}{25}
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3 years ago
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