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r-ruslan [8.4K]
3 years ago
11

Select the simplification that accurately explains the following statement.

Mathematics
1 answer:
aleksklad [387]3 years ago
3 0

Answer:

D

Step-by-step explanation:

1. Use property of exponents:

(a^b)^c=a^b\cdot ... \cdot a^b\ [\text{ take }c \text{ times } a^b]

Hence

(7^{\frac{1}{3}})^3=7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}

2. Use multiplication property of exponents:

a^b\cdot a^c=a^{b+c}

Thus,

7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}=7^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}

3. Since

\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=\frac{3}{3}=1,

we have that

7^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}=7^1=7

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