What is (8*320)^{1/3} ?

The solution to (8*320)^{1/3} is 8*5^{1/3}

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simplify (8*320)^{1/3}

simplify

(8 \cdot 320)^{\frac{1}{3}}

8 \cdot 5^{\frac{1}{3}}

Solution steps

(8 \cdot 320)^{\frac{1}{3}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(8 \cdot 320)^{\frac{1}{3}} = 8^{\frac{1}{3}} \cdot 32 0^{\frac{1}{3}}

= 8^{\frac{1}{3}} \cdot 32 0^{\frac{1}{3}}

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

= 2 \cdot 32 0^{\frac{1}{3}}

Prime factorization of

320 : 2^{6} \cdot 5

= 2 (2^{6} \cdot 5)^{\frac{1}{3}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(2^{6} \cdot 5)^{\frac{1}{3}} = (2^{6})^{\frac{1}{3}} \cdot 5^{\frac{1}{3}}

= 2 (2^{6})^{\frac{1}{3}} \cdot 5^{\frac{1}{3}}

(2^{6})^{\frac{1}{3}} = 4

= 2 \cdot 4 \cdot 5^{\frac{1}{3}}

Multiply the numbers:

2 \cdot 4 = 8

= 8 \cdot 5^{\frac{1}{3}}

\frac{- 5}{4 ^{2}}

5 x^{2} + 46 x - 40

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

3 x^{2} - 6 = - 54

98 = 3 y - 4