Answer
$$(5y^3)^3 \cdot \frac{(36y^{10})^1}{2}=\frac{4500y^{19}}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5y^3)^3\frac{(36y^{10})^1}{2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}125y^9\frac{(36y^{10})^1}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}125y^9\frac{36y^{10}}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{4500y^{19}}{2}\end{aligned} $$ | |
| ① | $$ \left( 5y^3 \right)^3 = 5^3 \left( y^3 \right)^3 = 125y^9 $$ |
| ② | A polynomial raised to the power of one equals itself. |
| ③ | Multiply $125y^9$ by $ \dfrac{36y^{10}}{2} $ to get $ \dfrac{ 4500y^{19} }{ 2 } $. Step 1: Write $ 125y^9 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 125y^9 \cdot \frac{36y^{10}}{2} & \xlongequal{\text{Step 1}} \frac{125y^9}{\color{red}{1}} \cdot \frac{36y^{10}}{2} \xlongequal{\text{Step 2}} \frac{ 125y^9 \cdot 36y^{10} }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4500y^{19} }{ 2 } \end{aligned} $$ |
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