Question

What is the following product? Assume x greater-than-or-equal-to 0

RootIndex 3 StartRoot x squared EndRoot times RootIndex 4 StartRoot x cubed EndRoot

A. x StartRoot x EndRoot
B. RootIndex 12 StartRoot x Superscript 5 EndRoot
C. x (RootIndex 12 StartRoot x Superscript 5 EndRoot)
D. x6

Answer 1

Which is the following product? Assume x ≥ 0

$\sqrt[3]{x^{2}} \times\sqrt[4]{x^{3}}$

A. $x\sqrt{x}$

B. $\sqrt[12]{x^{5}}$

C. $x\sqrt[12]{x^{5}}$

D. $x^{6}$

Answer:

C. $x\sqrt[12]{x^{5}}$

Step-by-step explanation:

NOTE : $\sqrt[n]{x^{m}}=x^{\frac{m}{n}}$

            $x^{a}\times x^{b}=x^{a+b}$

$\sqrt[3]{x^{2}} \times\sqrt[4]{x^{3}}$

$=x^{\frac{2}{3}}\times x^{\frac{3}{4}}$

$=x^{\frac{2}{3}+\frac{3}{4}}$

$=x^{\frac{2\times4+3\times3}{12}}$

$=x^{\frac{8+9}{12}}$

$=x^{\frac{17}{12}}$

$=x^{\frac{12+5}{12}}$

$=x^{\frac{12}{12}+\frac{5}{12}}$

$=x^{1+\frac{5}{12}}$

$=x\times x^{\frac{5}{12}}$

$=x\sqrt[12]{x^{5}}$

Answer 2

Answer:

c

Step-by-step explanation:

edge 2021