EVALUATE INTEGERS RAISED TO FRACTIONAL EXPONENTS WORKSHEET
About "Evaluate integers raised to fractional exponents worksheet"
Evaluate integers raised to fractional exponents worksheet :
Here we are going to see some practice questions on evaluating integers raised to rational exponents.
Step 1 :
Try to split the number which is in base as much as possible.
Step 2 :
Whenever we have power raised to another power, then we can multiply both the powers. If it is possible we can simplify.
Evaluate integers raised to fractional exponents worksheet - Questions
(1) Simplify 9^(1/2)
(2) Simplify 343^(-4/3)
(3) Simplify 36^(3/2)
(4) Simplify (81 m⁶)^(1/2)
(5) Simplify (64 n^12)^(1/6)
(6) Simplify (x^6)^(1/2)
(7) Simplify (9n^4)^(1/2)
(8) Simplify (27)^(1/6)
(9) Simplify (100)^(6/4)
(10) Simplify (64a^6)^(1/6)
Evaluate integers raised to fractional exponents worksheet - Solution
Question 1 :
Simplify 9^(1/2)
Solution :
We can write 9 as the multiple of 3,
9 = 3 x 3 = 3²
9^(1/2) = (3²)^(1/2)
= 3 ^(2 x 1/2)
= 3 ^1
= 3
Hence 3 is the answer.
Question 2 :
Simplify 343^(-4/3)
Solution :
We can write 343 as the multiple of 7,
343 = 7 x 7 x 7 = 7³
343^(-4/3) = (7³)^(-4/3)
= 7^3 x (-4/3)
= 7^-4
= 1/7^4
= 1/2401
Hence 1/2401 is the answer.
Question 3 :
Simplify 36^(3/2)
Solution :
We can express 36 as the multiple of 6,
36 = 6 x 6 = 6²
36^(3/2) = (6²)^(3/2)
= 6^2 x (3/2)
= 6^3
= 6 x 6 x 6
= 216
Hence 216 is the answer.
Question 4 :
Simplify (81 m⁶)^(1/2)
Solution :
We can express 81 as the multiple of 9,
81 = 9 x 9 = 9²
(81 m⁶)^(1/2) = (9²m⁶)^(1/2)
By distributing the power, we get
= (9²)^(1/2) (m⁶)^(1/2)
= 9 m^(6 x 1/2)
= 9 m^3
Hence 9 m^3 is the answer.
Question 5 :
Simplify (64 n^12)^(1/6)
Solution :
We can express 64 as the multiple of 2,
64 = 2 x 2 x 2 x 2 x 2 x 2 = 2⁶
(64 n^12)^(1/6) = (2⁶ n^12)^(1/6)
By distributing the power, we get
= (2⁶)^(1/6) (n^12)^(1/6)
= 2 n^(12 x 1/6)
= 2 n^2
Hence 2 n^2 is the answer.
Question 6 :
Simplify (x^6)^(1/2)
Solution :
= x^(6(1/2))
= x^3
Hence x^3 is the answer.
Question 7 :
Simplify (9n^4)^(1/2)
Solution :
We can express 9 as the multiple of 3,
9 = 3 x 3 = 3²
(9n^4)^(1/2) = (3²n^4)^(1/2)
By distributing the power, we get
= (3²)^(1/2) (n^4)^(1/2)
= 3^(2 x 1/2) (n^(4 x 1/2)
= 3 n^2
Hence 3 n^2 is the answer.
Question 8 :
Simplify (27)^(1/6)
Solution :
We can express 27 as the multiple of 3,
27 = 3 x 3 x 3 = 3³
(27)^(1/6) = ( 3³)^(1/6)
By multiplying the power raised to another power, we get
= 3^3 x (1/6)
= 3^(1/2)
= √3
Hence √3 is the answer.
Question 9 :
Simplify (100)^(6/4)
Solution :
We can express 100 as the multiple of 10,
100 = 10 x 10 = 10²
(100)^(6/4) = (10²)^(6/4)
= 10^2 x (6/4)
= 10^2 x (3/2)
= 10^3
= 10 x 10 x 10 = 1000
Hence the answer is 1000.
Question 10 :
Simplify (64a^6)^(1/6)
Solution :
We can express 64 as the multiple 2,
64 = 2 x 2 x 2 x 2 x 2 x 2
= 2^6
(64a^6)^(1/6) = (2^6a^6)^(1/6)
= (2a)^6^(1/6)
= 2a
Hence the answer is 2a.
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