1.95^6 x 10^6 divided by 2.56 x 10^-2
step by step
To divide the given numbers step by step, we can follow these steps:
1.95^6 x 10^6 / (2.56 x 10^-2)
First, let's simplify the power of 10 in the denominator:
10^-2 = 1/(10^2) = 1/100
Now, let's convert the division into multiplication by multiplying the numerator by the reciprocal of the denominator:
1.95^6 x 10^6 x 100 / (2.56)
Next, calculate 1.95^6:
1.95^6 = 44.109831
Applying this value:
44.109831 x 10^6 x 100 / 2.56
Now, multiply the exponent of 10 by the 100:
44.109831 x 10^(6+2) / 2.56
Since 10^8 is 100,000,000, rewrite the expression:
44.109831 x 100,000,000 / 2.56
Simplify the expression:
4,410,983,100 / 2.56
Now, divide the numbers:
4,410,983,100 ÷ 2.56 = 1,721,087,421.875
Therefore, 1.95^6 x 10^6 / 2.56 x 10^-2 = 1,721,087,421.875
To simplify the calculation, we can start by converting both numbers into scientific notation.
1.95^6 can be written as 1.95 x 10^6 (because 1.95^6 = 1.95 x 1.95 x 1.95 x 1.95 x 1.95 x 1.95).
Similarly, 2.56 x 10^-2 can be written as 0.0256 (by moving the decimal point two places to the left, as the negative exponent indicates dividing by a power of 10).
Now, the division problem can be rewritten as
(1.95 x 10^6) / (0.0256)
To divide the numbers, we divide the coefficients and subtract the exponents.
Dividing 1.95 by 0.0256 gives us 76.171875.
To subtract the exponents, we have 10^6 / 10^-2. Subtracting exponents means subtracting the negative exponent from the positive exponent, which gives us 10^(6-(-2)) = 10^8.
Therefore, the final answer is 76.171875 x 10^8, which can also be written as 7.6171875 x 10^9.
To solve the expression step by step, we can first simplify the numbers outside the exponent and the exponents separately.
1.95^6 is raised to the power of 6, which means multiplying 1.95 by itself 6 times:
1.95^6 = 1.95 * 1.95 * 1.95 * 1.95 * 1.95 * 1.95 = 27.30703125
10^6 means multiplying 10 by itself 6 times:
10^6 = 10 * 10 * 10 * 10 * 10 * 10 = 1,000,000
2.56 x 10^-2 means multiplying 2.56 by 10 raised to the power of -2:
2.56 x 10^-2 = 2.56 * 0.01 = 0.0256
Now we can substitute these values back into the original expression:
(27.30703125 x 1,000,000) / 0.0256
Next, we can multiply 27.30703125 by 1,000,000:
27.30703125 x 1,000,000 = 27,307,031.25
Finally, we can divide the result by 0.0256:
27,307,031.25 / 0.0256 = 1,066,894,379.88
Therefore, 1.95^6 x 10^6 divided by 2.56 x 10^-2 equals approximately 1,066,894,379.88.