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The problem is to evaluate the given exponents: a) $11^2$ b) $4^4$ c) $8^3$ d) $(\frac{4}{9})^2$ e) $0.8^2$ f) $0.2^4$

ArithmeticExponentsPowersCalculationsFractionsDecimals
2025/3/31

1. Problem Description

The problem is to evaluate the given exponents:
a) 11211^2
b) 444^4
c) 838^3
d) (49)2(\frac{4}{9})^2
e) 0.820.8^2
f) 0.240.2^4

2. Solution Steps

a) 112=11∗11=12111^2 = 11 * 11 = 121
b) 44=4∗4∗4∗4=16∗16=2564^4 = 4 * 4 * 4 * 4 = 16 * 16 = 256
c) 83=8∗8∗8=64∗8=5128^3 = 8 * 8 * 8 = 64 * 8 = 512
d) (49)2=49∗49=4∗49∗9=1681(\frac{4}{9})^2 = \frac{4}{9} * \frac{4}{9} = \frac{4*4}{9*9} = \frac{16}{81}
e) 0.82=0.8∗0.8=0.640.8^2 = 0.8 * 0.8 = 0.64
f) 0.24=0.2∗0.2∗0.2∗0.2=0.04∗0.04=0.00160.2^4 = 0.2 * 0.2 * 0.2 * 0.2 = 0.04 * 0.04 = 0.0016

3. Final Answer

a) 112=12111^2 = 121
b) 44=2564^4 = 256
c) 83=5128^3 = 512
d) (49)2=1681(\frac{4}{9})^2 = \frac{16}{81}
e) 0.82=0.640.8^2 = 0.64
f) 0.24=0.00160.2^4 = 0.0016

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