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MariettaO [177]
2 years ago
8

Applying properties of Exponents in exercise,use the properties of exponents to simplify the expression.See example 1.

Mathematics
1 answer:
Paladinen [302]2 years ago
5 0

Answer:  a) 1024, b) 1, c) 64 and d) 0.125.

Step-by-step explanation:

Since we have given that

(a) (4^3)(4^2)

As we know that

a^m\times a^n=a^{m+n}

So, it becomes,

4^3\times 4^2=4^{3+2}=4^5=1024

(b) (\dfrac{1}{4})^2(4^2)

As we know that

a^{-m}=\dfrac{1}{a^m}

(\dfrac{1}{4})^2(4^2)=4^-2\times 4^2=4^{-2+2}=4^0=1

c) (4^6)1/2

As we know that

(4^6)^{\frac{1}{2}}\\\\=4^{\frac{6}{2}}\\\\=4^3\\\\=64

(d) [(8^{-1})(8^{\frac{2}{3}})]^3

As we know that

[(8^{-1})(8^{\frac{2}{3}})]^3\\\\=[8^{-1+\frac{2}{3}}]^3\\\\=[8^{\frac{-1}{3}}]^3\\\\=8^{-1}\\\\=\dfrac{1}{8}=0.125

Hence, a) 1024, b) 1, c) 64 and d) 0.125.

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