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Popular >

simplify (27^{4/3})/(27^{2/3)}

Solution

simplify

\frac{2 7 ^{\frac{4}{3}}}{2 7 ^{\frac{2}{3}}}

Solution

9

Solution steps

\frac{2 7 ^{\frac{4}{3}}}{2 7 ^{\frac{2}{3}}}

Apply exponent rule:

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

= 2 7^{\frac{4}{3} - \frac{2}{3}}

Combine the fractions

\frac{4}{3} - \frac{2}{3} : \frac{2}{3}

= 2 7^{\frac{2}{3}}

Factor the number:

27 = 3^{3}

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}

(3^{3})^{\frac{2}{3}} = 3^{3 \cdot \frac{2}{3}} = 3^{2}

= 3^{2}

Refine

= 9

Popular Examples

16 x^{2} - 9 = 0

factor 4x^3+24x^2+32x factor

4 x^{3} + 24 x^{2} + 32 x

factor x^4+2x^3-23x^2-60x factor

x^{4} + 2 x^{3} - 23 x^{2} - 60 x

36x^2+7x=4-30x+7-6x^2

36 x^{2} + 7 x = 4 - 30 x + 7 - 6 x^{2}

2 x^{2} = 128

Frequently Asked Questions (FAQ)

What is (27^{4/3})/(27^{2/3)} ?
The solution to (27^{4/3})/(27^{2/3)} is 9