Solve ((2a ^ 5)/(3b ^ 4)) ^ 3 | 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

$$(\frac{2a^{5}}{3b^{4}})^{3}$$

Evaluate

$\frac{8a^{15}}{27b^{12}}$

Solution Steps

To raise $\frac{2a^{5}}{3b^{4}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2a^{5}\right)^{3}}{\left(3b^{4}\right)^{3}}$$

Expand $\left(2a^{5}\right)^{3}$.

$$\frac{2^{3}\left(a^{5}\right)^{3}}{\left(3b^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply $5$ and $3$ to get $15$.

$$\frac{2^{3}a^{15}}{\left(3b^{4}\right)^{3}}$$

Calculate $2$ to the power of $3$ and get $8$.

$$\frac{8a^{15}}{\left(3b^{4}\right)^{3}}$$

Expand $\left(3b^{4}\right)^{3}$.

$$\frac{8a^{15}}{3^{3}\left(b^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply $4$ and $3$ to get $12$.

$$\frac{8a^{15}}{3^{3}b^{12}}$$

Calculate $3$ to the power of $3$ and get $27$.

$$\frac{8a^{15}}{27b^{12}}$$

Expand

$\frac{8a^{15}}{27b^{12}}$

Solution Steps

To raise $\frac{2a^{5}}{3b^{4}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2a^{5}\right)^{3}}{\left(3b^{4}\right)^{3}}$$

Expand $\left(2a^{5}\right)^{3}$.

$$\frac{2^{3}\left(a^{5}\right)^{3}}{\left(3b^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply $5$ and $3$ to get $15$.

$$\frac{2^{3}a^{15}}{\left(3b^{4}\right)^{3}}$$

Calculate $2$ to the power of $3$ and get $8$.

$$\frac{8a^{15}}{\left(3b^{4}\right)^{3}}$$

Expand $\left(3b^{4}\right)^{3}$.

$$\frac{8a^{15}}{3^{3}\left(b^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply $4$ and $3$ to get $12$.

$$\frac{8a^{15}}{3^{3}b^{12}}$$

Calculate $3$ to the power of $3$ and get $27$.

$$\frac{8a^{15}}{27b^{12}}$$