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BabaBlast [244]
4 years ago
14

Which is equivalent

Mathematics
2 answers:
Citrus2011 [14]4 years ago
7 0

For this case we must find an expression equivalent to:

(x ^ {\frac {4} {3}} * x ^ {\frac {2} {3}}) ^ {\frac {1} {3}}

By definition of power properties we have to:

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

So, rewriting the expression we have:

x ^ {\frac {4} {3 * 3}} * x ^ {\frac {2} {3 * 3}} =

x ^ {\frac {4} {9}} * x ^ {\frac {2} {9}} =

By definition of multiplication of powers of the same base, we put the same base and add the exponents:

x ^ {\frac {4} {9} + \frac {2} {9}} =\\x ^ {\frac {4 + 2} {9}} =\\x ^ {\frac {6} {9}} =\\x ^ {\frac {2} {3}}

Answer:

Option B

Amanda [17]4 years ago
5 0

Answer:

x^{2/3}

Step-by-step explanation:

The question is on rules of rational exponents

Here we apply the formulae for product rule where;

= a^{n} *a^{t} = a^{n+t} \\\\\\\\=(x^{4/3} *x^{2/3} ) = x^{4/3 + 2/3} = x^{6/3} = x^{2} \\\\\\=(x^2)^{1/3} \\\\\\=\sqrt[3]{x^2}

=x^{2/3}

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