Answer
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}sqrt\frac{6x^3}{s}qrt\cdot3xsqrt\cdot8x^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6qrstx^3}{s}qrt\cdot3xsqrt\cdot8x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6q^2rstx^3}{s}rt\cdot3xsqrt\cdot8x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{6q^2r^2stx^3}{s}t\cdot3xsqrt\cdot8x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{6q^2r^2st^2x^3}{s}\cdot3xsqrt\cdot8x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{18q^2r^2st^2x^4}{s}sqrt\cdot8x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}18q^2r^2st^2x^4qrt\cdot8x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}18q^3r^2st^2x^4rt\cdot8x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} } }}}18q^3r^3st^2x^4t\cdot8x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle9}{\textcircled {9}} } }}}18q^3r^3st^3x^4\cdot8x^2 \xlongequal{ } \\[1 em] & \xlongequal{ }144q^3r^3st^3x^6\end{aligned} $$ | |
| ① | Multiply $qrst$ by $ \dfrac{6x^3}{s} $ to get $ \dfrac{ 6qrstx^3 }{ s } $. Step 1: Write $ qrst $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} qrst \cdot \frac{6x^3}{s} & \xlongequal{\text{Step 1}} \frac{qrst}{\color{red}{1}} \cdot \frac{6x^3}{s} \xlongequal{\text{Step 2}} \frac{ qrst \cdot 6x^3 }{ 1 \cdot s } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6qrstx^3 }{ s } \end{aligned} $$ |
| ② | Multiply $ \dfrac{6qrstx^3}{s} $ by $ q $ to get $ \dfrac{ 6q^2rstx^3 }{ s } $. Step 1: Write $ q $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{6qrstx^3}{s} \cdot q & \xlongequal{\text{Step 1}} \frac{6qrstx^3}{s} \cdot \frac{q}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 6qrstx^3 \cdot q }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6q^2rstx^3 }{ s } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{6q^2rstx^3}{s} $ by $ r $ to get $ \dfrac{ 6q^2r^2stx^3 }{ s } $. Step 1: Write $ r $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{6q^2rstx^3}{s} \cdot r & \xlongequal{\text{Step 1}} \frac{6q^2rstx^3}{s} \cdot \frac{r}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 6q^2rstx^3 \cdot r }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6q^2r^2stx^3 }{ s } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{6q^2r^2stx^3}{s} $ by $ t $ to get $ \dfrac{ 6q^2r^2st^2x^3 }{ s } $. Step 1: Write $ t $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{6q^2r^2stx^3}{s} \cdot t & \xlongequal{\text{Step 1}} \frac{6q^2r^2stx^3}{s} \cdot \frac{t}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 6q^2r^2stx^3 \cdot t }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6q^2r^2st^2x^3 }{ s } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{6q^2r^2st^2x^3}{s} $ by $ 3x $ to get $ \dfrac{ 18q^2r^2st^2x^4 }{ s } $. Step 1: Write $ 3x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{6q^2r^2st^2x^3}{s} \cdot 3x & \xlongequal{\text{Step 1}} \frac{6q^2r^2st^2x^3}{s} \cdot \frac{3x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 6q^2r^2st^2x^3 \cdot 3x }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 18q^2r^2st^2x^4 }{ s } \end{aligned} $$ |
| ⑥ | Multiply $ \dfrac{18q^2r^2st^2x^4}{s} $ by $ s $ to get $ 18q^2r^2st^2x^4$. Step 1: Write $ s $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Cancel $ \color{red}{ s } $ in first and second fraction. Step 3: Multiply numerators and denominators. Step 4: Simplify numerator and denominator. $$ \begin{aligned} \frac{18q^2r^2st^2x^4}{s} \cdot s & \xlongequal{\text{Step 1}} \frac{18q^2r^2st^2x^4}{s} \cdot \frac{s}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{18q^2r^2st^2x^4}{\color{red}{1}} \cdot \frac{\color{red}{1}}{1} = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 18q^2r^2st^2x^4 \cdot 1 }{ 1 \cdot 1 } \xlongequal{\text{Step 4}} \frac{ 18q^2r^2st^2x^4 }{ 1 } =18q^2r^2st^2x^4 \end{aligned} $$ |
| ⑦ | $$ 18 q^2 r^2 s t^2 x^4 q = 18 q^{2 + 1} r^{2} s t^{2} x^{4} = 18 q^3 r^2 s t^2 x^4 $$ |
| ⑧ | $$ 18 q^3 r^2 s t^2 x^4 r = 18 q^{3} r^{2 + 1} s t^{2} x^{4} = 18 q^3 r^3 s t^2 x^4 $$ |
| ⑨ | $$ 18 q^3 r^3 s t^2 x^4 t = 18 q^{3} r^{3} s t^{2 + 1} x^{4} = 18 q^3 r^3 s t^3 x^4 $$ |