Simplify \({25}^{2}\) to \(625\).
\[\frac{4}{3}\times \frac{22}{7}{r}^{3}+43692=\frac{0}{7}\times 625\times 49\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{4\times 22{r}^{3}}{3\times 7}+43692=\frac{0}{7}\times 625\times 49\]
Simplify \(4\times 22{r}^{3}\) to \(88{r}^{3}\).
\[\frac{88{r}^{3}}{3\times 7}+43692=\frac{0}{7}\times 625\times 49\]
Simplify \(3\times 7\) to \(21\).
\[\frac{88{r}^{3}}{21}+43692=\frac{0}{7}\times 625\times 49\]
Simplify \(\frac{0}{7}\) to \(0\).
\[\frac{88{r}^{3}}{21}+43692=0\times 625\times 49\]
Simplify \(0\times 625\times 49\) to \(0\).
\[\frac{88{r}^{3}}{21}+43692=0\]
Subtract \(43692\) from both sides.
\[\frac{88{r}^{3}}{21}=-43692\]
Multiply both sides by \(21\).
\[88{r}^{3}=-43692\times 21\]
Simplify \(43692\times 21\) to \(917532\).
\[88{r}^{3}=-917532\]
Divide both sides by \(88\).
\[{r}^{3}=-\frac{917532}{88}\]
Simplify \(\frac{917532}{88}\) to \(\frac{20853}{2}\).
\[{r}^{3}=-\frac{20853}{2}\]
Take the cube root of both sides.
\[r=\sqrt[3]{-\frac{20853}{2}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[r=\frac{\sqrt[3]{-20853}}{\sqrt[3]{2}}\]
Simplify exponent.
\[r=\frac{-27.524716}{\sqrt[3]{2}}\]
Move the negative sign to the left.
\[r=-\frac{27.524716}{\sqrt[3]{2}}\]
Decimal Form: -21.846382
r=-27.524716071386/2^(1/3)
