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babymother [125]
3 years ago
11

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:

<u>Properties of Exponents</u>

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

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

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

<em>Hence, the length of HG is 5mm</em>

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.
6 0
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.<br><br> (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)


6 0
3 years ago
Solve the inequality | x + 5/3 | -3 &gt; 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
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