Practice problems on exponents
Introduction
Let n be a positive integer. x * x * x * x …………. Upto n terms is written as x n. Here x is called the base and n is called the exponents or index or power. We can read x n as x power n. or x raised to the power n. The operation that can be done between the exponents are as follows:
(i) x n * x m = x m+n
(ii)` x ^n / x ^m` = x n – m
(iii) (x n) m = xnm
(iv) (xy) n = x n . yn
(v)` (x / y ) ^n` = `x ^ n / y ^ n`
(vi) x˚ = 1
Now you can solve the problems given below using the above formula on practice problems on exponents.
The practice problems on exponents.
1. Evaluate the following:
(i) `8 ^ (5/ 3)`
[Ans: 32]
(ii)`27 ^ (2 / 3)`
[Ans: 9]
(iii) `9 ^ (3 / 2)`
[Ans: 27]
(iv) `8 ^ (-4 / 3)`
[Ans: `1 / 16` ]
(v)` (243) ^ (-3 / 5)`
[Ans: `1 / 27` ]
2. Simplify the following:
(i) `(27 / 125) ^ (2 / 3)`
[Ans: `5 / 3` ]
(ii) `(16 / 81) ^( - 3 / 4) xx (49 / 9) -: ( 343 / 216) ^ (2 / 3)`
[Ans: `27 / 2` ]
(iii) `((3 ^ -4) / (2 ^ - 8)) ^ (1 / 4)`
[Ans: `4 / 3` ]
(iv) `(27 ^ -3 / 9 ^ -3) ^ (1 / 5)`
[Ans: 3 ^ (-3 / 5)]
(v) `(32) ^ (- 2 / 5) -: (125) ^( -2 / 3)`
[Ans: `25 / 4` ]
More practice problems on exponents.
3. Simplify:
(i) `((y ^p) /( y ^ -q)) ^ (p ^2 ** pq + q ^2) xx ((y ^q) /( y ^ -r) )^(q ^2 ** qr + r ^2) xx (y ^r / y ^ -p) ^ (r ^2 ** rp + p^2)`
[Ans: 1]
4. If a = x m + n . y l, b = x n + l . y m and C = x l + m . y n, show that a ^ m-n . b ^ n –l . c ^ l – m = 1.
5. Solve for x:
(i) `9 xx 3 ^x = (27) ^(2x ** 5 )`
[Ans: x = `17 / 5` ]
(ii) `sqrt [(3 / 5) ^ (1**2x)]` = `4 17 / 27`
[Ans: x = `7 / 2` ]
Let n be a positive integer. x * x * x * x …………. Upto n terms is written as x n. Here x is called the base and n is called the exponents or index or power. We can read x n as x power n. or x raised to the power n. The operation that can be done between the exponents are as follows:
(i) x n * x m = x m+n
(ii)` x ^n / x ^m` = x n – m
(iii) (x n) m = xnm
(iv) (xy) n = x n . yn
(v)` (x / y ) ^n` = `x ^ n / y ^ n`
(vi) x˚ = 1
Now you can solve the problems given below using the above formula on practice problems on exponents.
The practice problems on exponents.
1. Evaluate the following:
(i) `8 ^ (5/ 3)`
[Ans: 32]
(ii)`27 ^ (2 / 3)`
[Ans: 9]
(iii) `9 ^ (3 / 2)`
[Ans: 27]
(iv) `8 ^ (-4 / 3)`
[Ans: `1 / 16` ]
(v)` (243) ^ (-3 / 5)`
[Ans: `1 / 27` ]
2. Simplify the following:
(i) `(27 / 125) ^ (2 / 3)`
[Ans: `5 / 3` ]
(ii) `(16 / 81) ^( - 3 / 4) xx (49 / 9) -: ( 343 / 216) ^ (2 / 3)`
[Ans: `27 / 2` ]
(iii) `((3 ^ -4) / (2 ^ - 8)) ^ (1 / 4)`
[Ans: `4 / 3` ]
(iv) `(27 ^ -3 / 9 ^ -3) ^ (1 / 5)`
[Ans: 3 ^ (-3 / 5)]
(v) `(32) ^ (- 2 / 5) -: (125) ^( -2 / 3)`
[Ans: `25 / 4` ]
More practice problems on exponents.
3. Simplify:
(i) `((y ^p) /( y ^ -q)) ^ (p ^2 ** pq + q ^2) xx ((y ^q) /( y ^ -r) )^(q ^2 ** qr + r ^2) xx (y ^r / y ^ -p) ^ (r ^2 ** rp + p^2)`
[Ans: 1]
4. If a = x m + n . y l, b = x n + l . y m and C = x l + m . y n, show that a ^ m-n . b ^ n –l . c ^ l – m = 1.
5. Solve for x:
(i) `9 xx 3 ^x = (27) ^(2x ** 5 )`
[Ans: x = `17 / 5` ]
(ii) `sqrt [(3 / 5) ^ (1**2x)]` = `4 17 / 27`
[Ans: x = `7 / 2` ]