3-17/8-14
To simplify the expression 3-17/8-14, we must follow the order of operations, which is parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).
First, we can evaluate the division: 17/8 = 2.125.
Now the expression becomes: 3-2.125-14.
Next, we subtract 2.125 from 3: 3 - 2.125 = 0.875.
Finally, we subtract 14 from 0.875: 0.875 - 14 = -13.125.
Therefore, 3-17/8-14 = -13.125.
(7^-3)^7x7^20/6^-2
To simplify the expression (7^-3)^7 × 7^20 / 6^-2, we can begin by simplifying each exponent separately and then apply the rules of exponents.
First, let's simplify the exponents within the parentheses: (7^-3)^7 = 7^(-3 × 7) = 7^-21.
Now the expression becomes:
7^-21 × 7^20 / 6^-2
We can apply the rule of exponents that states that a^m × a^n = a^(m + n):
7^-21 × 7^20 = 7^(-21 + 20) = 7^-1
Next, we can apply the rule of exponents that states that a^m / a^n = a^(m - n):
7^-1 / 6^-2 = 7^(-1 - (-2)) = 7^1 × 6^2 = 42^2 = 1764.
Therefore, (7^-3)^7 × 7^20 / 6^-2 simplifies to 1764.
12^-5x12^7
To simplify the expression 12^-5 × 12^7, we can apply the rule of exponents that states a^m × a^n = a^(m + n).
Using this rule, we can add the exponents together:
12^-5 × 12^7 = 12^(-5 + 7) = 12^2.
Therefore, 12^-5 × 12^7 simplifies to 12^2.
To solve the expression 3-17/8-14 step-by-step, follow the order of operations (PEMDAS/BODMAS):
1. Perform division: 17/8 = 2.125
The expression now becomes: 3 - 2.125 - 14
2. Perform the subtraction operation from left to right:
3 - 2.125 = 0.875
The expression now becomes: 0.875 - 14
3. Perform the subtraction operation again:
0.875 - 14 = -13.125
So, the final result of the expression 3-17/8-14 is -13.125.
To solve the expression 3-17/8-14, you need to follow the order of operations, which is commonly known as PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction).
Let's break down the calculation step by step:
1. Start with division: 17 divided by 8 equals 2.125.
2. Now, the expression becomes: 3 - 2.125 - 14.
3. Next, subtract 2.125 from 3: 3 - 2.125 equals 0.875.
4. Lastly, subtract 14 from 0.875: 0.875 - 14 equals -13.125.
So, the answer to the expression 3-17/8-14 is -13.125.