(7^-3)^7
(7^-3)^7 is equal to (1/7^3)^7.
To simplify this, we can use the property of exponents that states (a^m)^n is equal to a^(m*n).
Therefore, (1/7^3)^7 simplifies to 1/7^(3*7), which is equal to 1/7^21.
(7^-3)^7 Multiply your exponents first.
Certainly! When multiplying exponents, we can use the property that states (a^m)^n is equal to a^(m*n).
Applying this property to (7^-3)^7, we can simplify it as follows:
(7^-3)^7 = 7^(-3*7)
Simplifying the exponent, we have:
7^(-3*7) = 7^(-21)
Thus, (7^-3)^7 is equal to 7^(-21).
-3*7
-3*7 is equal to -21.
(7−3)^7 ⋅ 7^20/6^−2
To simplify the expression (7−3)^7 ⋅ 7^20/6^−2, we can follow the order of operations.
First, let's simplify (7 - 3)^7:
(7 - 3)^7 = 4^7
Next, let's simplify 7^20:
7^20 = 7^(2 * 10) = (7^2)^10 = 49^10
Lastly, let's simplify 6^(-2):
6^(-2) = 1/6^2 = 1/36
Now we can rewrite the expression:
(7 - 3)^7 ⋅ 7^20/6^−2 = 4^7 ⋅ 49^10 / 1/36
To multiply the powers that have the same base, we add the exponents:
4^7 = 4^(1*7) = (4^1)^7 = 4^7
Similarly,
49^10 = 49^(1*10) = (49^1)^10 = 49^10
Now we can substitute these simplified bases back into the expression:
4^7 ⋅ 49^10 / 1/36 = 4^7 ⋅ 49^10 * 36/1
Finally, we can calculate the result:
4^7 = 16384
49^10 = 5,764,801,229,311,314,000,000,000
36/1 = 36
Therefore, the simplified expression is 16384 ⋅ 5,764,801,229,311,314,000,000,000 * 36.
nope
I apologize for the incorrect response. Let's start again.
To simplify (7 - 3)^7 ⋅ 7^20/6^(-2), we can follow the order of operations.
First, let's simplify (7 - 3)^7:
(7 - 3)^7 = 4^7
Next, let's simplify 7^20:
7^20 = 7^(2 * 10) = (7^2)^10 = 49^10
Now, let's simplify 6^(-2):
6^(-2) = 1 / 6^2 = 1 / 36
Now, let's substitute these values back into the expression:
(7 - 3)^7 ⋅ 7^20 / 6^(-2) = 4^7 ⋅ 49^10 / 1/36
Now we can calculate the result:
4^7 = 16384
49^10 = 282,475,249
1/36 = 0.0277778
Therefore, the simplified expression is:
16384 ⋅ 282,475,249 / 0.0277778
After calculating this expression, we would get the final result.
no the answer is 36/7
I apologize for the confusion. Let's simplify the expression again:
(7 - 3)^7 ⋅ 7^20 / 6^-2
First, let's simplify (7 - 3)^7:
4^7
Next, let's simplify 7^20:
7^20
Now let's simplify 6^-2:
1 / 6^2 = 1 / 36
Now substitute these simplified values back into the expression:
4^7 ⋅ 7^20 / (1 / 36)
To simplify further, let's remove the division by multiplying by the reciprocal:
4^7 ⋅ 7^20 * 36
To calculate the result, let's evaluate each term separately:
4^7 = 16384
7^20 = 79766443076872509863361
36
Multiplying these terms together, we get:
16384 ⋅ 79766443076872509863361 ⋅ 36
After calculating this expression, the simplified answer is obtained.
15⋅8^0/5+4(7^0−6)
Let's simplify the expression step by step:
First, let's simplify the exponent 8^0. Any number (except 0) raised to the power of 0 is equal to 1.
8^0 = 1
Next, let's simplify the exponent 7^0. Similar to the above, any number (except 0) raised to the power of 0 is equal to 1.
7^0 = 1
Now, let's substitute these simplified values back into the expression:
15 ⋅ 8^0 / 5 + 4(1 - 6)
Next, we calculate the parentheses:
15 ⋅ 8^0 / 5 + 4(-5)
Now, let's continue evaluating the expression:
15 ⋅ 1 / 5 + 4 (-5)
15 / 5 + (-20)
Now, we can perform the division and addition/subtraction:
3 + (-20)
Finally, we can simplify:
3 - 20
And the final answer is:
-17
no its 12
I apologize for the incorrect response.
Let's reassess the expression:
15⋅8^0/5 + 4(7^0−6)
First, let's simplify the exponents:
8^0 = 1
7^0 = 1
Now, we substitute these simplified values back into the expression:
15⋅1/5 + 4(1−6)
Next, let's simplify within parentheses:
15⋅1/5 + 4(-5)
Now, perform the multiplications and additions/subtractions:
15/5 + (-20)
3 + (-20)
Finally, we can simplify:
3 - 20
The final answer is indeed -17, not 12. Apologies for my previous incorrect response.