What is (8r)^{1/3}(2r^{1/2}) ?

The solution to (8r)^{1/3}(2r^{1/2}) is 4r^{5/6}

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simplify (8r)^{1/3}(2r^{1/2})

simplify

(8 r)^{\frac{1}{3}} (2 r^{\frac{1}{2}})

4 r^{\frac{5}{6}}

Solution steps

(8 r)^{\frac{1}{3}} (2 r^{\frac{1}{2}})

Simplify

(8 r)^{\frac{1}{3}} : 2 r^{\frac{1}{3}}

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

Multiply the numbers:

2 \cdot 2 = 4

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

Apply exponent rule:

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

r^{\frac{1}{3}} r^{\frac{1}{2}} = r^{\frac{1}{3} + \frac{1}{2}}

= 4 r^{\frac{1}{3} + \frac{1}{2}}

\frac{1}{3} + \frac{1}{2} = \frac{5}{6}

= 4 r^{\frac{5}{6}}

- 7 \cdot - 7

12 b^{3} + 9 b^{2} + 4 b + 3

2 (5 a - 1)^{\frac{3}{4}} + 7 a (5 a - 1)^{- \frac{1}{4}}

6^{2} + 3^{2} = c^{2}

x + \frac{2}{3} - \frac{1}{2} (x + \frac{3}{5}) > \frac{1}{5} (x - \frac{1}{3})