Problem 1 :
Evaluate :
(-1)4
Problem 2 :
Evaluate :
(-1)5
Problem 3 :
Evaluate :
-(-3)3
Problem 4 :
Evaluate :
50
Problem 5 :
Evaluate :
-30
Problem 6 :
Evaluate :
(-7)0
Problem 7 :
Evaluate :
5-3
Problem 8 :
Evaluate :
23 ⋅ 32 ⋅ (-1)5
Problem 9 :
Evaluate :
(-1)4 ⋅ 33 ⋅ 22
Problem 10 :
If x2y3 = 10 and x3y2 = 8, then find the value of x5y5.
1. Answer :
(-1)4
Order of operations (PEMDAS) dictates that parentheses take precedence.
Here, the exponent 4 is an even number. So, the negative sign inside the parentheses will become positive.
When 1 is multiplied by itself any number of times, the result will be 1.
More clearly,
(-1)4 = (-1) ⋅ (-1) (-1) ⋅ (-1)
(-1)4 = 1
2. Answer :
(-1)5
Order of operations (PEMDAS) dictates that parentheses take precedence.
Here, the exponent 5 is an odd number. So, the negative sign inside the parentheses will remain same.
When 1 is multiplied by itself any number of times, the result will be 1.
More clearly,
(-1)5 = (-1) ⋅ (-1) ⋅ (-1) ⋅ (-1) ⋅ (-1)
(-1)4 = -1
3. Answer :
-(-3)3
Order of operations (PEMDAS) dictates that parentheses take precedence.
-[(-3)3] = -[(-3) ⋅ (-3) ⋅ (-3)]
-[(-3)3] = -[-27]
-[(-3)3] = 27
4. Answer :
50
Anything to the power zero is equal to 1.
So, we have
50 = 1
5. Answer :
-30
Anything to the power zero is equal to 1.
So, we have
-30 = -1
6. Answer :
(-7)0
Order of operations (PEMDAS) dictates that parentheses take precedence.
Anything to the power zero is equal to 1.
So, we have
(-7)0 = 1
7. Answer :
5-3
Using laws of exponents, we have
5-3 = 1/53
5-3 = 1/125
8. Answer :
23 ⋅ 32 ⋅ (-1)5
In the above expression, first evaluate each term separately.
23 = 2 ⋅ 2 ⋅ 2 = 8
32 = 3 ⋅ 3 = 9
(-1)5 = (-1) ⋅ (-1) ⋅ (-1) ⋅ (-1) ⋅ (-1) = -1
Now, we have
23 ⋅ 32 ⋅ (-1)5 = 8 ⋅ 9 ⋅ (-1)
23 ⋅ 32 ⋅ (-1)5 = -72
9. Answer :
In the above expression, first evaluate each term separately.
(-1)4 = (-1) ⋅ (-1) ⋅ (-1) ⋅ (-1) = 1
33 = 3 ⋅ 3 ⋅ 3 = 27
22 = 2 ⋅ 2 = 4
Now, we have
(-1)4 ⋅ 33 ⋅ 22 = 1 ⋅ 27 ⋅ 4
(-1)4 ⋅ 33 ⋅ 22 = 108
10. Answer :
x2y3 = 10 ----(1)
x3y2 = 8 ----(2)
Multiply (1) and (2) :
(1) ⋅ (2) ----> (x2y3) ⋅ (x3y2) = 10 ⋅ 8
x5y5 = 80
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