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horsena [70]
3 years ago
11

Which of the following is the simplified form of ^7 radical x • ^7 radical x • ^7 radical x

Mathematics
2 answers:
schepotkina [342]3 years ago
6 0

For this case we must find an expression equivalent to:

\sqrt [7] {x} * \sqrt [7] {x} * \sqrt [7] {x}

By definition of properties of powers and roots we have:

\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}

So, rewriting the given expression we have:

x ^ {\frac {1} {7}} * x ^ {\frac {1} {7}} * x ^ {\frac {1} {7}} =

To multiply powers of the same base we put the same base and add the exponents:

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

Answer:

Option 1

Alona [7]3 years ago
4 0

Answer: Option 1.

Step-by-step explanation:

We need to remember that:

\sqrt[n]{a^m}=a^{\frac{m}{n}}

Then, having the expression:

\sqrt[7]{x}*\sqrt[7]{x} *\sqrt[7]{x}

We can rewrite it in this form:

=x^{\frac{1}{7}}*x^{\frac{1}{7}} *x^{\frac{1}{7}}

According to the Product of powers property:

(a^m)(a^n)=a^{(m+n)}

Then, the simplied form of the given expression, is:

=x^{(\frac{1}{7}+\frac{1}{7}+\frac{1}{7})}=x^\frac{3}{7}

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