Simplify 4 to the 7th over 5 squared all raised to the 3rd power.
4 to the 10th over 5 to the 5th
4 to the 4th over 5
4 to the 21st over 5 to the 6th
12 to the 7th over 15 squared
To simplify the expression (4^7 / 5^2)^3, we can first simplify the numerator and denominator separately, and then raise the result to the power of 3.
Let's start with the numerator:
4^7 means 4 raised to the power of 7.
To calculate this, we multiply 4 by itself 7 times: 4 * 4 * 4 * 4 * 4 * 4 * 4.
The result is 16384.
Next, let's simplify the denominator:
5^2 means 5 raised to the power of 2.
To calculate this, we multiply 5 by itself 2 times: 5 * 5.
The result is 25.
Now, we have (16384 / 25)^3.
To simplify this further, we'll raise the fraction to the power of 3.
To raise a fraction to a power, we raise both the numerator and denominator to that power:
(16384^3) / (25^3)
To calculate 16384^3, we multiply 16384 by itself 3 times: 16384 * 16384 * 16384.
The result is 4,398,046,511,104.
To calculate 25^3, we multiply 25 by itself 3 times: 25 * 25 * 25.
The result is 15,625.
Therefore, the expression simplifies to:
4,398,046,511,104 / 15,625
To simplify the expression, we can follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
The expression can be written as:
((4^7) / (5^2))^3
Step 1: Simplify the numerator: 4^7 = 16384
Step 2: Simplify the denominator: 5^2 = 25
The expression becomes:
(16384 / 25)^3
Step 3: Simplify the enclosed expression: 16384 / 25 = 655.36
The expression becomes:
(655.36)^3
Step 4: Evaluate the expression: (655.36)^3 = 288,717,436.16
Therefore, the simplified expression is:
288,717,436.16
multiply the exponents
for example, (2^3)^5 = 2^(3*5) = 2^15
why?
2^3 = 2*2*2
(2^3)^5 = 2*2*2 * 2*2*2 * 2*2*2 * 2*2*2 * 2*2*2
^ is just shorthand for ***...
Just as * is shorthand for +++...
2*3*4 = 2+2+2 + 2+2+2 + 2+2+2 + 2+2+2