I have 27x^4 = 1.1 x 10^-36
I have to figure out what X equals.
The answer is x= 4.5 x 10^-10
How do you get that for the answer??
look for a button on your scientific calculator labeled
Exp
enter
1.1
Exp
36
± , that key makes your exponent entry negative
÷
27 =
(you should get 4.074...x 10^-38
√
=
√
=
I got 4.4926.... x 10^-10
which is their answer.
why do you square root it twice?
we had to take the fourth root of ^(1/4)
?^(1/4)
= [ (?^(1/24) ]^(1/2)
e. g. the fourth root of 81 is 3
so take √81 to get 9
then √9 = 3
so to take the 8th root, I would take √ three times consecutively.
ok, so what if you have
4x^3 = 2.80 x 10^-9
what would x equal in this case and how would you get it?
I really appreciate ur help. As you can tell i am slightly confused. Ur explanations are helping greatly.
To solve the equation 27x^4 = 1.1 x 10^-36 and find the value of x, follow these steps:
1. Divide both sides of the equation by 27 to isolate the x^4 term:
(27x^4) / 27 = (1.1 x 10^-36) / 27
Simplifying, we get x^4 = (1.1 x 10^-36) / 27.
2. Rewrite 1.1 x 10^-36 as a decimal number:
1.1 x 10^-36 = 0.0000000...0011 (36 zeros before the 11)
3. Continue simplifying the equation:
x^4 = 0.0000000...0011 / 27
Rearranging, we have x^4 = (0.0000000...0011) * (1 / 27)
Since (1 / 27) can also be expressed as 27^(-1), we can replace it as x^4 = (0.0000000...0011) * (27^(-1)).
4. Now we can take the fourth root of both sides to solve for x:
(x^4)^(1/4) = [(0.0000000...0011) * (27^(-1))]^(1/4)
Simplifying, we obtain x = [(0.0000000...0011)^(1/4)] * [(27^(-1))^(1/4)].
5. Calculate each part separately:
- Evaluate (0.0000000...0011)^(1/4):
- To find the fourth root of a decimal, you can use a calculator or software. It equals approximately 0.133.
- Evaluate (27^(-1))^(1/4):
- First, we simplify (27^(-1)):
27^(-1) equals 1/27, which can be written as 0.03703703... (repeating decimal).
- To find the fourth root of 0.03703703..., you can use a calculator or software. It equals approximately 0.5.
6. Plug in the calculated values to solve for x:
x = 0.133 * 0.5
x = 0.0665
7. Finally, express the answer in scientific notation:
x = 6.65 x 10^-2
Thus, the correct solution to the equation 27x^4 = 1.1 x 10^-36 is x = 6.65 x 10^-2.