Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{x^{25}x\cdot4}\cdot5\frac{x}{3x\cdot3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5}{4x^{26}}\frac{x}{9x} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{5x}{36x^{27}}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{1}{4x^{26}} $ by $ 5 $ to get $ \dfrac{ 5 }{ 4x^{26} } $. Step 1: Write $ 5 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{1}{4x^{26}} \cdot 5 & \xlongequal{\text{Step 1}} \frac{1}{4x^{26}} \cdot \frac{5}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot 5 }{ 4x^{26} \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5 }{ 4x^{26} } \end{aligned} $$ |
| ② | $$ 3 x \cdot 3 = 9 x $$ |
| ③ | Multiply $ \dfrac{5}{4x^{26}} $ by $ \dfrac{x}{9x} $ to get $ \dfrac{ 5x }{ 36x^{27} } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{5}{4x^{26}} \cdot \frac{x}{9x} & \xlongequal{\text{Step 1}} \frac{ 5 \cdot x }{ 4x^{26} \cdot 9x } \xlongequal{\text{Step 2}} \frac{ 5x }{ 36x^{27} } \end{aligned} $$ |