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.
3-17/8-14
5 answers
(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.
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.
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.