Solve ((- 3a ^ 5)/(b ^ 4)) ^ 6 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(\frac{-3a^{5}}{b^{4}})^{6}$$

Evaluate

$\frac{729a^{30}}{b^{24}}$

Solution Steps

To raise $\frac{-3a^{5}}{b^{4}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-3a^{5}\right)^{6}}{\left(b^{4}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply $4$ and $6$ to get $24$.

$$\frac{\left(-3a^{5}\right)^{6}}{b^{24}}$$

Expand $\left(-3a^{5}\right)^{6}$.

$$\frac{\left(-3\right)^{6}\left(a^{5}\right)^{6}}{b^{24}}$$

To raise a power to another power, multiply the exponents. Multiply $5$ and $6$ to get $30$.

$$\frac{\left(-3\right)^{6}a^{30}}{b^{24}}$$

Calculate $-3$ to the power of $6$ and get $729$.

$$\frac{729a^{30}}{b^{24}}$$

Expand

$\frac{729a^{30}}{b^{24}}$

Solution Steps

To raise $\frac{-3a^{5}}{b^{4}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-3a^{5}\right)^{6}}{\left(b^{4}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply $4$ and $6$ to get $24$.

$$\frac{\left(-3a^{5}\right)^{6}}{b^{24}}$$

Expand $\left(-3a^{5}\right)^{6}$.

$$\frac{\left(-3\right)^{6}\left(a^{5}\right)^{6}}{b^{24}}$$

To raise a power to another power, multiply the exponents. Multiply $5$ and $6$ to get $30$.

$$\frac{\left(-3\right)^{6}a^{30}}{b^{24}}$$

Calculate $-3$ to the power of $6$ and get $729$.

$$\frac{729a^{30}}{b^{24}}$$