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Tom [10]
3 years ago
5

What is done to exponents when you add or subtract powers having the same base?

Mathematics
2 answers:
Gennadij [26K]3 years ago
8 0
You keep the same exponent when adding or subtracting
statuscvo [17]3 years ago
6 0
One of the base in the numberical equation changes to a lesser power, causing it to change. Such as 4 to the power of 3 minus 2 to the power of 3 = 6 so basically the exponents disappear and the base is left with no exponent.
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1. Simplify. 5–1(3–2)
konstantin123 [22]

Answer with explanation:

Using following law of indices

1.x^a \times x^b=x^{a+b}\\\\2. (x^m)^n=x^{mn}\\\\ 3. x^{-n}=\frac{1}{x^n}\\\\4. \frac{x^m}{x^n}=x^{m-n}

1.5^{-1}\times 3^{-2}=\frac{1}{5}\times\frac{1}{3^2}\\\\=\frac{1}{5\times9}\\\\=\frac{1}{45}\\\\2. \frac{mn^{-4}}{p^0*q^{-2}}=\frac{mq^2}{n^4}\\\\ 3.0.0042=4.2\times 10^3\\\\4.6.12 \times 10^3=6.12 \times 1000=6120\\\\ 5.0.5 \times(8\times10^5})=\frac{1}{2}\times8 \times 10^5=4\times 10^5\\\\6. (9 \times 10^3)^2=9^2 \times (10^3)^2=81 \times 10^6\\\\7.( \frac{1}{2}a^{-4}\times b^2 )_{a=-2,b=4}{\text{or}}( \frac{1}{2}a^{4}\times b^{-2} )_{a=-2,b=4}=\frac{1}{2}\times (-2)^{-4}\times(4)^2{\text{or}}=\frac{1}{2}\times (-2)^{4}\times(4)^{-2}=\frac{16}{2\times16}=\frac{1}{2}

9. (4\times x\times y^2)^3\times (xy)^5=4^3\times x^3\times (y^2)^3\times x^5 \times y^5\\\\=64\times x^{3+5}\times y^{5+6}\\\\=64x^8y^{11}\\\\10.(2\times t^3)^3(0.4\times r)^2=2^3 \times (t^3)^3\times (0.4)^2 \times r^2=8\times t^9 \times 0.16 \times r^2=1.28r^2t^9

8. A number raised to a negative exponent is negative.

Explaining with the help of few examples

 1.2^{-3}=\frac{1}{2^3}=\frac{1}{8}\\\\ 2.(-3)^{-3}=\frac{1}{(-3)^{3}}=\frac{-1}{27}

Option C: Sometimes

1.Option B

2.Option A

3.Option C

4.Option A

5.Option D

6.  81 \times 10^6

7.Option B

8.Option C

9.Option A

10.Option  1.28 r^2 \times t^9

4 0
3 years ago
Read 2 more answers
Which function has an axis of x=-2
coldgirl [10]

Give me the whole question including information, and graphs.

8 0
3 years ago
For each table, determine whether it shows that x and y are proportional.
myrzilka [38]

9514 1404 393

Answer:

  1. proportional, 6

  2. not proportional

Step-by-step explanation:

<u>Table 1</u>

Each y-value is 6 times the corresponding x-value, so the variables are proportional, and y = 6 times x.

<u>Table 2</u>

The ratios of y to x are 2, 4, 8, so are not the same. The values are not proportional.

8 0
2 years ago
Dennis made a scale drawing of his backyard using the scale 1/4 inch =3 feet the rectangular swimming pool was 2 inches long and
seraphim [82]
(1/4)x = 2 

x = 8 x 3 = 24 feet long

(1/4)x = 1

x = 4 x 3 = 12 feet wide

24ft x 12ft = 288ft^2
3 0
2 years ago
(1,-3) (2,2) <br> finding the Slope
Llana [10]
The slope of (1,-3) and (2,2) is 5
3 0
2 years ago
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