Question

simplify:
$(2x) ^{ \frac{1}{2} } \times (2x ^{3} ) ^{ \frac{3}{2} }$
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Answer 1

Answer:

$\huge\boxed{(2x)^\frac{1}{2}\times(2x^3)^\frac{3}{2}=4x^5}$

Step-by-step explanation:

$(2x)^\frac{1}{2}\times(2x^3)^\frac{3}{2}\qquad\text{use}\ (ab)^n=a^nb^m\\\\=2^\frac{1}{2}x^\frac{1}{2}\times2^\frac{3}{2}(x^3)^\frac{3}{2}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^\frac{1}{2}x^\frac{1}{2}\times2^\frac{2}{3}x^{(3)(\frac{3}{2})}=2^\frac{1}{2}x^\frac{1}{2}\times2^\frac{2}{3}x^\frac{9}{2}\\\\\text{use the commutative and associative property}\\\\=\left(2^\frac{1}{2}\times2^\frac{3}{2}\right)\left(x^\frac{1}{2}\times x^\frac{9}{2}\right)\qquad\text{use}\ a^n\times a^m=a^{n+m}$

$=2^{\frac{1}{2}+\frac{3}{2}}x^{\frac{1}{2}+\frac{9}{2}}=2^\frac{1+3}{2}x^{\frac{1+9}{2}}=2^\frac{4}{2}x^\frac{10}{2}=2^2x^5=4x^5$

Answer 2

Answer:

$4x^5$

Step-by-step explanation:

$(2x)^\frac{1}{2} \times (2x^3)^\frac{3}{2} =$

$= (2x)^\frac{1}{2} \times (2x \times x^2)^\frac{3}{2}$

$= [(2x)^\frac{1}{2} \times (2x)^\frac{3}{2}] \times (x^2)^\frac{3}{2}$

$= (2x)^{\frac{1}{2} + \frac{3}{2}} \times x^{{2} \times \frac{3}{2}}$

$= (2x)^{\frac{4}{2}} \times x^{\frac{6}{2}}$

$= 2^2x^2 \times x^3$

$= 4x^5$