mplify as a whole number: 22⋅332^2\cdot3^32
2
⋅3
3
To simplify the expression, we can first simplify the exponents.
22⋅(3^2)^2⋅3^3 = 22⋅3^4⋅3^3 = 22⋅3^7
Now, we can multiply the numbers and simplify the expression further.
22⋅3^7 = 22⋅2187 = 48014
Therefore, the simplified expression is 48014.
To simplify the expression 22⋅(332^2)⋅(3^32) / (2⋅3^3), we follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).
Let's simplify each part of the expression:
1. Simplify the exponents:
(332^2) = 110,224
(3^32) = 15,937,424,543,125
2. Simplify the division:
(2 / 2) = 1
(3^3) = 27
3. Multiply the remaining terms:
22⋅110,224⋅15,937,424,543,125⋅1⋅27 = 7,818,329,025,293,000
Therefore, the simplified expression is 7,818,329,025,293,000.
To simplify the given expression, we need to use the rules of exponents and simplification of powers.
Let's break down the given expression step by step:
22⋅332^2⋅3^32⋅3
First, we can simplify the expression 332^2. To do this, we square 332, which results in 110,224.
So, the expression becomes:
22⋅110,224⋅3^32⋅3
Next, we can simplify 3^32⋅3 by adding the exponents 32 and 1, which gives us 3^33.
Now, the expression becomes:
22⋅110,224⋅3^33
To simplify 3^33, we can calculate the value of 3 raised to the power of 33. This can be done by multiplying 3 by itself 33 times.
Using calcualtor:
3^33 ≈ 3.8742049e+15
So, the expression becomes:
22⋅110,224⋅3.8742049e+15
Finally, we can multiply 22 and 110,224 together and then multiply the result by 3.8742049e+15.
Using a calculator:
22⋅110,224⋅3.8742049e+15 ≈ 9.15003557e+20
Therefore, the simplified form of the expression is approximately 9.15003557e+20.