What is 3/4 (2)^{4/3} ?

The solution to 3/4 (2)^{4/3} is 3/(2^{2/3)}

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simplify 3/4 (2)^{4/3}

simplify

\frac{3}{4} (2)^{\frac{4}{3}}

\frac{3}{2 ^{\frac{2}{3}}}

Decimal Notation

1.88988 \dots

Solution steps

\frac{3}{4} \cdot 2^{\frac{4}{3}}

2^{\frac{4}{3}} = 2 \cdot 2^{\frac{1}{3}}

= 2 \cdot 2^{\frac{1}{3}} \cdot \frac{3}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 \cdot 2 \cdot 2 ^{\frac{1}{3}}}{4}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{6 \cdot 2 ^{\frac{1}{3}}}{4}

Cancel the common factor:

2

= \frac{3 \cdot 2 ^{\frac{1}{3}}}{2}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{\frac{1}{3}}}{2} = \frac{1}{2 ^{1 - \frac{1}{3}}}

= \frac{3}{2 ^{1 - \frac{1}{3}}}

Subtract the numbers:

1 - \frac{1}{3} = \frac{2}{3}

= \frac{3}{2 ^{\frac{2}{3}}}

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