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

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 _.

## This Post Has 8 Comments

1. jeanieb says:

We are given

$\frac{(4.1\times 10^{3})(2.8\times 10^{-7})}{(3.1\times 10^{-5})}$

We can move like terms altogether

$\frac{(4.1\times 10^{3})(2.8\times 10^{-7})}{(3.1\times 10^{-5})}=\frac{4.1\times 2.8}{3.1}\times \frac{10^{3}\times 10^{-7}}{10^{-5}}$

now, we can use property of exponent

$a^m\times a^n=a^{m+n}$

$=\frac{4.1\times 2.8}{3.1}\times \frac{10^{3-7}}{10^{-5}}$

We can use another exponent property

$\frac{a^m}{a^n} =a^{m-n}$

so, we get

$=\frac{4.1\times 2.8}{3.1}\times 10^{3-7+5}$

$=\frac{4.1\times 2.8}{3.1}\times 10^{1}$

$=3.70323\times 10^{1}$

So, the result in scientific notation is

$=3.70323\times 10^{1}$..........Answer

So, the result as a decimal is

$=37.0323$.............Answer

2. Expert says:

3. globalremix says:

$2.25 \times 10^{6}$

2250000

Step-by-step explanation:

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

Now, $(1.5 \times 10^{3} )^{2}$

= $(1.5 \times 10^{3} ) \times (1.5 \times 10^{3} )$

= $(1.5 \times 1.5) \times (10^{3} \times 10^{3} )$

= $2.25 \times 10^{(3+3)}$

= $2.25 \times 10^{6}$

So, this is the answer in scientific notation.

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

4. Expert says:

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

5. bhhh7351 says:

$6.561*10^{-7}\\0.0000006561$

The explanation is shown below:

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

$(8.1*10^{-4})^2$

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

$65.61*10^{-8}=6.561*10^{-7}$

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

$0.0000006561$

6. staffordkimberly says:

Consider the expression $(8.1\cdot 10^{-4})^2.$

Use main properties for powers:

1. $(a\cdot b)^m=a^m\cdot b^m;$

2. $(a^m)^n=a^{m\cdot n};$

3. $a^m\cdot a^n=a^{m+n}.$

Then

$(8.1\cdot 10^{-4})^2=8.1^2\cdot (10^{-4})^2=65.61\cdot 10^{-4\cdot 2}=65.61\cdot 10^{-8}=6,561\cdot 10^{-2}\cdot 10^{-8}=6,561\cdot 10^{-10}.$

The result in scientific notation is $6,561\cdot 10^{-10}.$

The result as a decimal is $0.0000006561.$

7. shawn20034 says:

8. 341404143 says:

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