Summary Exercise of Exponents + Answers

SMAK 1 BPK PENABUR

Exponent, Surds & Logarithm Exercise
10’th Grade – Champion Class Pg 33
2026 - 2027
1. Determine the value(s) of 𝑥 from the following
equations:
Simplifying exponential expressions & A. 43𝑥−6 = 64 (3)
solving exponential equations 2 +3𝑥+4 3
B. 52𝑥 = 625 (− 2 𝑜𝑟 0)
Pg 10 2. Solve the equation 27𝑥−2 − 2433𝑥 = 0. (− 2)
1


1. Simplify the following expressions: 3. Determine the value(s) of 𝑥 from the following
23 ×24 equations:
A. 25
(4)
𝑥
3𝑥𝑦 6 A. 7(√3) − 3𝑥 = −18 (4)
B. (3𝑥𝑦)
𝑦5 B. 25𝑥−1 + 4(5𝑥 ) − 21 = 0 (1)
2
66 5. Determine the value(s) of 𝑥 so that
C. (25 ×34 ) (324) 2 2
− 1
2 9𝑥 + 4𝑥 = 37.
3 3 𝑜𝑟 8) (27
5𝑎 5 𝑏4
D. ( 𝑎3 𝑏 ) (25𝑎4 𝑏 6 ) 6. One of solution to the equation
22𝑥+𝑝 − 2𝑥+𝑝 = 9.2𝑥 − 2 is 𝑥 = 1. Determine:
2. Find the value of 𝑥 and 𝑦 from the following A. The value of 𝑝. (3)
equations: B. The other solution(s). (−3)
A. (32 )5 = 3𝑥 (10)
B. (53 )𝑥 = 512 (4)
Additional Questions
C. (𝑏 2 )4 = 𝑏 𝑥 (8)
82𝑛−3 .2𝑛−3
D. (52 𝜋)3 = 5𝑥 𝜋 𝑦 (6 & 3) 1. Simplify .
4.22−𝑛
7𝑛−16
A. 2 D. 28𝑛−16
3. Determine the result of :
1 B. 28𝑛−8 E. 28𝑛−4
A. (5𝑎2 𝑏 3 )0 × 2−2 (4)
C. 27𝑛−8
−3 3 8
B. 6 ×4 (27)
2 𝑝2 𝑞−3 𝑟 𝑝𝑞𝑟
C. 6(−3)−4 ( ) 2. Simplify (𝑝−5 𝑞𝑟 −2 ) (𝑝3 𝑞−4 𝑟3 ) .
27
6
D. (192) 𝑝5 𝑟
2−5 A. 𝑝5 𝑞𝑟 D. 𝑞5
𝑝5 𝑞
5. Simplify and write your answer in positive exponent B. 𝑝9 𝑞𝑟 5 E. 𝑟3
form. 𝑝5 𝑟
1 C.
A. (3𝑎)−2 (9𝑎2 ) 𝑞

3
B. (3𝑦 4 )
𝑦 −4 𝑎 −2 −𝑏 −2
3. Simplify 𝑎−1 −𝑏−1 .
𝑎 2 𝑏−3 𝑎7
C. ( 2) 𝑎𝑏 𝑎−𝑏
𝑎 −5 𝑏−1 𝑏 A. D.
−3 𝑎−𝑏 𝑎𝑏
𝑎2 27
D. (3𝑏−3 ) (𝑎6 𝑏9 ) B.
𝑎𝑏
E.
𝑏−𝑎
𝑏−𝑎 𝑎𝑏
𝑎+𝑏
C.
6. Simplify and write your answer in positive exponent 𝑎𝑏
form.
2(52 )+3(52 ) 27𝑎3 𝑏 −2 𝑐
−2
𝑎 2 𝑏𝑐 −1
2
A. (55 ) 4. Simplify ( ) ( ) .
5−2 36𝑎4 𝑏3 4𝑎 −2 𝑏4
−3
𝑥 2 𝑦 −5 𝑦 24
B. (𝑥 −5 𝑦3 ) (𝑥 21 ) 9𝑎2 9𝑎 10 𝑏4
A. 256𝑏16
D. 𝑐2
2
(4𝑎 −6 𝑏3 ) 2 9𝑎 2
C. 8𝑎 12 𝑏6
(𝑎24 ) B. 16𝑏16
E. 9𝑎10 𝑏4 𝑐 2
𝑎 10 𝑏4
C. 9𝑐 4



SMAK 1 BPK PENABUR JIMMY HARYANTO