All categories

3 years ago

5^10/5^3 rewrite in the form of 5^n

Mathematics

1 answer:

Sergeeva-Olga [200]3 years ago

5 0

Answer:

5^7

Step-by-step explanation:

To rewrite the expression, you use the laws of exponents.

Using the law of exponents of division, you subtract the exponent of the smaller value (5^3) from the larger value (5^10).

Your expression would now be this:

5^10-3

Since the bases have the same value (5), they remain the same.

As a result of 5^10-3, you would get 5^7 as your answer.

To check that both are equivalent to each other you solve and find the values of both expressions.

5^7=78125

5^10/5^3=78125

5^7=5^10/5^3

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Simplify. (Assume all variables represent positive real numbers). Leave answer in radical form.

Flauer [41]

Answer:

$\sqrt{128a^{6}b^{13}} = 8 a^{3} b^{6} \sqrt{2b}$

Step-by-step explanation:

Given

$\sqrt{128a^{6}b^{13}}$

Required

Solve

$\sqrt{128a^{6}b^{13}}$

The expression can be split to:

$\sqrt{128a^{6}b^{13}} = \sqrt{128} * \sqrt{a^{6}} * \sqrt{b^{13}}$

$\sqrt{128a^{6}b^{13}} = \sqrt{64 * 2} * \sqrt{a^{6}} * \sqrt{b^{13}}$

$\sqrt{128a^{6}b^{13}} = \sqrt{64} * \sqrt{2} * \sqrt{a^{6}} * \sqrt{b^{13}}$

$\sqrt{128a^{6}b^{13}} = \sqrt{64} * \sqrt{2} * \sqrt{a^{6}} * \sqrt{b^{12 + 1}}$

$\sqrt{128a^{6}b^{13}} = \sqrt{64} * \sqrt{2} * \sqrt{a^{6}} * \sqrt{b^{12}} * \sqrt{b}$

So, we have:

$\sqrt{128a^{6}b^{13}} = 8 * \sqrt{2} * a^{6/2} * b^{12/2} * \sqrt{b}$

$\sqrt{128a^{6}b^{13}} = 8 * \sqrt{2} * a^{3} * b^{6} * \sqrt{b}$

Rewrite as:

$\sqrt{128a^{6}b^{13}} = 8 * a^{3} * b^{6}* \sqrt{2} * \sqrt{b}$

$\sqrt{128a^{6}b^{13}} = 8 a^{3} b^{6}* \sqrt{2b}$

$\sqrt{128a^{6}b^{13}} = 8 a^{3} b^{6} \sqrt{2b}$

5 0

2 years ago

What is 0.368 written in expanded form?

Goshia [24]

There are two methods that can be used to write 0.368 in expanded form.

Method-1:

Take the first number after the decimal point and divide it by 10. Take the second number after the decimal point and divide it by 100. Take the third number after the decimal point and divide it by 1000. Lastly, add all of them.

$\frac{3}{10} + \frac{6}{100} + \frac{8}{1000} = 0.368$

Method-2:
Multiply first number after decimal point with 0.1; multiply second number after decimal point with 0.01; multiply third number after decimal point with 0.001, and add them all.

(3 * 0.1) + (6 * 0.01) + (8 * 0.001) = 0.368

3 0

3 years ago

Whats the value of the 5 in 453,193

Nataly [62]

453,193 400,000+ 50,000 +3,000+ 100 +90+ 3=453,193 so it is ten thousand 10,000=50,000

6 0

3 years ago

Read 2 more answers

Which linear function rule models the table below? (0,6) (5,9) (10,12) (15,15)

Dovator [93]

Answer:

y= 0.6x + 6 or y= 3/5x + 6

Step-by-step explanation:

The function for a linear function is y=mx+b.

We know that b is 6 because that is the y-intercept.

However to find m we need to see how much the x coordinates skip on the table and the y coordinates. We can see that x coordinates skip by 5s and the y corrdinates skip by 3. We than divide 3/5 to get o.6 and we get the equation. This video, tittled "Writing A Linear Equation From A Function Table" explains it much better than I can.

6 0

3 years ago

The area of the rectangular garden is 38 1/4 square meters the width of the garden is 4 1/2meters find the length of the garden

faltersainse [42]

Answer:

Area = Length * Width

38 1/4 = L * 4 1/2

L = (38 1/4)/(4 1/2) = (153/4)/(9/2) = (153 * 2)/(4 * 9) = 17 1/2

Step-by-step explanation:

6 0

3 years ago