Apply the laws of exponents, calculate the result and express the result in scientific notation, and as a decimal: (8.1*10^-4)^2 format your answer like this: the result of the scientific notation is __* the result as a decimal is _.

Skip to content# Apply the laws of exponents, calculate the result and express the result in scientific

Mathematics ##
Comments (8) on “Apply the laws of exponents, calculate the result and express the result in scientific”

### Leave a Reply Cancel reply

Apply the laws of exponents, calculate the result and express the result in scientific notation, and as a decimal: (8.1*10^-4)^2 format your answer like this: the result of the scientific notation is __* the result as a decimal is _.

We are given

[tex]\frac{(4.1\times 10^{3})(2.8\times 10^{-7})}{(3.1\times 10^{-5})}[/tex]

We can move like terms altogether

[tex]\frac{(4.1\times 10^{3})(2.8\times 10^{-7})}{(3.1\times 10^{-5})}=\frac{4.1\times 2.8}{3.1}\times \frac{10^{3}\times 10^{-7}}{10^{-5}}[/tex]

now, we can use property of exponent

[tex]a^m\times a^n=a^{m+n}[/tex]

[tex]=\frac{4.1\times 2.8}{3.1}\times \frac{10^{3-7}}{10^{-5}}[/tex]

We can use another exponent property

[tex]\frac{a^m}{a^n} =a^{m-n}[/tex]

so, we get

[tex]=\frac{4.1\times 2.8}{3.1}\times 10^{3-7+5}[/tex]

[tex]=\frac{4.1\times 2.8}{3.1}\times 10^{1}[/tex]

[tex]=3.70323\times 10^{1}[/tex]

So, the result in scientific notation is

[tex]=3.70323\times 10^{1}[/tex]..........Answer

So, the result as a decimal is

[tex]=37.0323[/tex].............Answer

answer is x<

[tex]2.25 \times 10^{6}[/tex]

2250000

Step-by-step explanation:

We have to express the result of [tex](1.5 \times 10^{3} )^{2}[/tex] in scientific notation and as a decimal.

Now, [tex](1.5 \times 10^{3} )^{2}[/tex]

= [tex](1.5 \times 10^{3} ) \times (1.5 \times 10^{3} )[/tex]

= [tex](1.5 \times 1.5) \times (10^{3} \times 10^{3} )[/tex]

= [tex]2.25 \times 10^{(3+3)}[/tex]

= [tex]2.25 \times 10^{6}[/tex]

So, this is the answer in scientific notation.

And in decimal notation, it can be written as 2250000.

(Answer)

40%=2/550=1/230=3/1056=14/25

The answer is:

[tex]6.561*10^{-7}\\0.0000006561[/tex]

The explanation is shown below:

1. You have the following expression given in the problem above:

[tex](8.1*10^{-4})^2[/tex]

2. By applying the properties of exponents, the power rule, you can multiply the power 2 by and the power -4, then:

[tex]65.61*10^{-8}=6.561*10^{-7}[/tex]

3. To write as a decimal, you must move the decimal point 7 places to the left. Therefore, you have:

[tex]0.0000006561[/tex]

Consider the expression [tex](8.1\cdot 10^{-4})^2.[/tex]

Use main properties for powers:

1. [tex](a\cdot b)^m=a^m\cdot b^m;[/tex]

2. [tex](a^m)^n=a^{m\cdot n};[/tex]

3. [tex]a^m\cdot a^n=a^{m+n}.[/tex]

Then

[tex](8.1\cdot 10^{-4})^2=8.1^2\cdot (10^{-4})^2=65.61\cdot 10^{-4\cdot 2}=65.61\cdot 10^{-8}=6,561\cdot 10^{-2}\cdot 10^{-8}=6,561\cdot 10^{-10}.[/tex]

The result in scientific notation is [tex]6,561\cdot 10^{-10}.[/tex]

The result as a decimal is [tex]0.0000006561.[/tex]

The answer is 2250000.

the result in scientific notation is 6.561×10⁻⁷the result as a decimal is 0.000 000 656 1Explanation:

The rules of exponents say the exponent outside parentheses applies to each factor inside parentheses.

... (8.1*10^-4)^2 = 8.1^2 × (10^-4)^2

... = 65.61 × 10^-8

... = 6.561 × 10^-7 . . . . adjust to scientific notation with one digit left of the decimal point

The exponent of -7 means the decimal point in the decimal number is 7 places to the left of where it is in scientific notation. That is ...

... 6.561 × 10^-7 = 0.0000006561