Solve t^3/2+1152t^4/3*t^-1/2

$$t ^ { 3 / 2 } + 1152 t ^ { 4 / 3 } \times t ^ { - 1 / 2 }$$

Factor

$$\left(t^{\frac{2}{3}}+1152\right)t^{\frac{5}{6}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{4}{3} and -\frac{1}{2} to get \frac{5}{6}.

$$factor(t^{\frac{3}{2}}+1152t^{\frac{5}{6}})$$

Factor out t^{\frac{5}{6}}.

$$t^{\frac{5}{6}}\left(t^{\frac{2}{3}}+1152\right)$$

Evaluate

$$\left(t^{\frac{2}{3}}+1152\right)t^{\frac{5}{6}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{4}{3} and -\frac{1}{2} to get \frac{5}{6}.

$$t^{\frac{3}{2}}+1152t^{\frac{5}{6}}$$