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3 years ago

Use operations of exponent to simplify 3^5/3^-6

Mathematics

1 answer:

7nadin3 [17]3 years ago

3 0

Answer:

$\displaystyle \frac{3^5}{3^{-6}}=3^{11}$

Step-by-step explanation:

Properties of Exponents

They can be used to simplify expressions of the form

$b^x\cdot b^y=b^{x+y}$

$\displaystyle \frac{b^x}{b^y}=b^{x-y}$

The last property will be used to simplify:

$\displaystyle \frac{3^5}{3^{-6}}=3^{5-(-6)}=3^{5+6}=3^{11}$

$\mathbf{\displaystyle \frac{3^5}{3^{-6}}=3^{11}}$

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What is the length of HG?

Leviafan [203]

Answer:

$HG = 5$

Step-by-step explanation:

Given

$HE = 8mm$

$EF = 12mm$

$Area = 68mm^2$

Find the length of HG

First, it should be noted that the displayed figure is a trapezium

The area of a trapezium is calculated by multiplying the sum of parallel sides by half its height;

In this case;

$Area = \frac{HG + EF}{2} * HE$

Substitute the values of Area, HE and EF

$68 = \frac{HG + 12}{2} * 8$

$68 = (HG + 12) * 4$

Divide both sides by 4

$\frac{68}{4} = \frac{(HG + 12) * 4}{4}$

$17 = HG + 12$

Subtract 12 from both sides

$17 - 12 = HG + 12 - 12$

$5 = HG$

$HG = 5$

Hence, the length of HG is 5mm

6 0

3 years ago

On your lab bench, you have 2 mystery metal cubes. each cube has a mass of 10.0 grams. cube a has a density of 10 g/cm3. cube b

lianna [129]

To compare both, we find the volume of both cubes as follows:

V of cube A = 10 g / 10 g/cm^3 = 1 cm^3

V of cube B = 10 g / 0.37 g/cm^3 = 27 cm^3

I think the correct answer from the choices listed above is option D. Each edge of cube b is three times larger than cube. Hope this helps. Have a nice day.

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3 years ago

6x+x-8=6x+6 solve the equation for x

marysya [2.9K]

Answer:

x = 14

Step-by-step explanation:

6x+x-8=6x+6

Combine like terms

7x -8 = 6x+6

Subtract 6x from each side

7x-6x-8=6x-6x+6

x-8 = 6

Add 8 to each side

x-8+8 = 6+8

x = 14

5 0

3 years ago

Write in expanded form. Use parentheses to indicate multiplication. (2 r ) 5

olasank [31]

Answer: $(2r)^{5}=(2r)(2r)(2r)(2r)(2r)$

Step-by-step explanation:

1. To solve the exercise shown in the problem, you must remember that the exponent 5 indicates the number of times $2r$ is used as a factor. Therefore, it is used as a factor five times.

2. Therefore, keeping the information above on mind, you have that you can write the expanded form of $(2r)^{5}$ as following:

$(2r)^{5}=(2r)(2r)(2r)(2r)(2r)$

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3 years ago

Solve the inequality | x + 5/3 | -3 > 6

horrorfan [7]

Answer

The solution to the inequality is x > 22/3 or x < -32/3

Explanation

The given inequality is:

$|x+\frac{5}{3}|-3>6$

The inequality can be solved as follows:

$\begin{gathered} |x+\frac{5}{3}|-3>6 \\ \\ Take-3\text{ }to\text{ }the\text{ }other\text{ }side\text{ }of\text{ }the\text{ }inequality\text{ }sign \\ \\ |x+\frac{5}{3}|>6+3 \\ \\ |x+\frac{5}{3}|>9 \end{gathered}$

Now, split the absolute value into two inequalities, for case > 9 or < -9

$\begin{gathered} x+\frac{5}{3}>9\text{ }or\text{ }x+\frac{5}{3}9-\frac{5}{3}\text{ }or\text{ }x\frac{22}{3}\text{ }or\text{ }x$

Hence the solution to the inequality | x + 5/3 | -3 > 6 is x > 22/3 or x < -32/3

5 0

1 year ago