What is \sqrt[5]{8}^{a+3}*\sqrt[5]{4x}^{2-a} ?

The solution to \sqrt[5]{8}^{a+3}*\sqrt[5]{4x}^{2-a} is 2^{(a+13)/5}x^{(-a+2)/5}

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simplify \sqrt[5]{8}^{a+3}*\sqrt[5]{4x}^{2-a}

simplify

2^{\frac{a + 13}{5}} x^{\frac{- a + 2}{5}}

Solution steps

= 8^{\frac{a + 3}{5}} (4 x)^{\frac{2 - a}{5}}

(4 x)^{\frac{2 - a}{5}} = 4^{\frac{2 - a}{5}} x^{\frac{2 - a}{5}}

= 8^{\frac{a + 3}{5}} \cdot 4^{\frac{- a + 2}{5}} x^{\frac{- a + 2}{5}}

Factor integer

8 = 2^{3}

= (2^{3})^{\frac{a + 3}{5}} \cdot 4^{\frac{2 - a}{5}} x^{\frac{2 - a}{5}}

Apply exponent rule:

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

(2^{3})^{\frac{a + 3}{5}} = 2^{3 \cdot \frac{a + 3}{5}}

= 2^{3 \cdot \frac{a + 3}{5}} \cdot 4^{\frac{2 - a}{5}} x^{\frac{2 - a}{5}}

Refine

= 2^{\frac{3 ( a + 3 )}{5}} \cdot 4^{\frac{2 - a}{5}} x^{\frac{2 - a}{5}}

Factor integer

4 = 2^{2}

= 2^{\frac{3 ( a + 3 )}{5}} (2^{2})^{\frac{2 - a}{5}} x^{\frac{2 - a}{5}}

Apply exponent rule:

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

(2^{2})^{\frac{2 - a}{5}} = 2^{2 \cdot \frac{2 - a}{5}}

= 2^{\frac{3 ( a + 3 )}{5}} \cdot 2^{2 \cdot \frac{2 - a}{5}} x^{\frac{2 - a}{5}}

Refine

= 2^{\frac{3 ( a + 3 )}{5}} \cdot 2^{\frac{2 ( 2 - a )}{5}} x^{\frac{2 - a}{5}}

Apply exponent rule:

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

2^{\frac{3 ( a + 3 )}{5}} \cdot 2^{\frac{2 ( 2 - a )}{5}} = 2^{\frac{3 ( a + 3 )}{5} + \frac{2 ( - a + 2 )}{5}}

= 2^{\frac{3 ( a + 3 )}{5} + \frac{2 ( 2 - a )}{5}} x^{\frac{2 - a}{5}}

Apply rule

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

= 2^{\frac{3 ( a + 3 ) + 2 ( 2 - a )}{5}} x^{\frac{2 - a}{5}}

2^{\frac{3 ( a + 3 ) + 2 ( 2 - a )}{5}} = 2^{\frac{a + 13}{5}}

= 2^{\frac{a + 13}{5}} x^{\frac{- a + 2}{5}}

(x - a)^{2} (x - b)^{2}

(4.48 \cdot 1 0^{- 23}) (6.02214 \cdot 1 0^{23})

\frac{1}{3} \cdot 3.14 \cdot 1 4^{2} \cdot 14

4 x^{3 a} y^{2} \cdot (\frac{3}{8} x^{a} y^{3})

What is \sqrt[5]{8}^{a+3}*\sqrt[5]{4x}^{2-a} ?
The solution to \sqrt[5]{8}^{a+3}*\sqrt[5]{4x}^{2-a} is 2^{(a+13)/5}x^{(-a+2)/5}