Solve ((3p ^ 2)/(4q ^ 3)) ^ 4 * ((2q ^ 5)/(3p ^ 3)) ^ 5 | 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

$$(\frac{3p^{2}}{4q^{3}})^{4}\times(\frac{2q^{5}}{3p^{3}})^{5}$$

Evaluate

$\frac{q^{13}}{24p^{7}}$

Solution Steps

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

$$\frac{\left(3p^{2}\right)^{4}}{\left(4q^{3}\right)^{4}}\times \left(\frac{2q^{5}}{3p^{3}}\right)^{5}$$

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

$$\frac{\left(3p^{2}\right)^{4}}{\left(4q^{3}\right)^{4}}\times \frac{\left(2q^{5}\right)^{5}}{\left(3p^{3}\right)^{5}}$$

Multiply $\frac{\left(3p^{2}\right)^{4}}{\left(4q^{3}\right)^{4}}$ times $\frac{\left(2q^{5}\right)^{5}}{\left(3p^{3}\right)^{5}}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3p^{2}\right)^{4}\times \left(2q^{5}\right)^{5}}{\left(4q^{3}\right)^{4}\times \left(3p^{3}\right)^{5}}$$

Expand $\left(3p^{2}\right)^{4}$.

$$\frac{3^{4}\left(p^{2}\right)^{4}\times \left(2q^{5}\right)^{5}}{\left(4q^{3}\right)^{4}\times \left(3p^{3}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $4$ to get $8$.

$$\frac{3^{4}p^{8}\times \left(2q^{5}\right)^{5}}{\left(4q^{3}\right)^{4}\times \left(3p^{3}\right)^{5}}$$

Calculate $3$ to the power of $4$ and get $81$.

$$\frac{81p^{8}\times \left(2q^{5}\right)^{5}}{\left(4q^{3}\right)^{4}\times \left(3p^{3}\right)^{5}}$$

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

$$\frac{81p^{8}\times 2^{5}\left(q^{5}\right)^{5}}{\left(4q^{3}\right)^{4}\times \left(3p^{3}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply $5$ and $5$ to get $25$.

$$\frac{81p^{8}\times 2^{5}q^{25}}{\left(4q^{3}\right)^{4}\times \left(3p^{3}\right)^{5}}$$

Calculate $2$ to the power of $5$ and get $32$.

$$\frac{81p^{8}\times 32q^{25}}{\left(4q^{3}\right)^{4}\times \left(3p^{3}\right)^{5}}$$

Multiply $81$ and $32$ to get $2592$.

$$\frac{2592p^{8}q^{25}}{\left(4q^{3}\right)^{4}\times \left(3p^{3}\right)^{5}}$$

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

$$\frac{2592p^{8}q^{25}}{4^{4}\left(q^{3}\right)^{4}\times \left(3p^{3}\right)^{5}}$$

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

$$\frac{2592p^{8}q^{25}}{4^{4}q^{12}\times \left(3p^{3}\right)^{5}}$$

Calculate $4$ to the power of $4$ and get $256$.

$$\frac{2592p^{8}q^{25}}{256q^{12}\times \left(3p^{3}\right)^{5}}$$

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

$$\frac{2592p^{8}q^{25}}{256q^{12}\times 3^{5}\left(p^{3}\right)^{5}}$$

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

$$\frac{2592p^{8}q^{25}}{256q^{12}\times 3^{5}p^{15}}$$

Calculate $3$ to the power of $5$ and get $243$.

$$\frac{2592p^{8}q^{25}}{256q^{12}\times 243p^{15}}$$

Multiply $256$ and $243$ to get $62208$.

$$\frac{2592p^{8}q^{25}}{62208q^{12}p^{15}}$$

Cancel out $2592p^{8}q^{12}$ in both numerator and denominator.

$$\frac{q^{13}}{24p^{7}}$$

Expand

$\frac{q^{13}}{24p^{7}}$

Solution Steps

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

$$\frac{\left(3p^{2}\right)^{4}}{\left(4q^{3}\right)^{4}}\times \left(\frac{2q^{5}}{3p^{3}}\right)^{5}$$

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

$$\frac{\left(3p^{2}\right)^{4}}{\left(4q^{3}\right)^{4}}\times \frac{\left(2q^{5}\right)^{5}}{\left(3p^{3}\right)^{5}}$$

Multiply $\frac{\left(3p^{2}\right)^{4}}{\left(4q^{3}\right)^{4}}$ times $\frac{\left(2q^{5}\right)^{5}}{\left(3p^{3}\right)^{5}}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3p^{2}\right)^{4}\times \left(2q^{5}\right)^{5}}{\left(4q^{3}\right)^{4}\times \left(3p^{3}\right)^{5}}$$

Expand $\left(3p^{2}\right)^{4}$.

$$\frac{3^{4}\left(p^{2}\right)^{4}\times \left(2q^{5}\right)^{5}}{\left(4q^{3}\right)^{4}\times \left(3p^{3}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $4$ to get $8$.

$$\frac{3^{4}p^{8}\times \left(2q^{5}\right)^{5}}{\left(4q^{3}\right)^{4}\times \left(3p^{3}\right)^{5}}$$

Calculate $3$ to the power of $4$ and get $81$.

$$\frac{81p^{8}\times \left(2q^{5}\right)^{5}}{\left(4q^{3}\right)^{4}\times \left(3p^{3}\right)^{5}}$$

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

$$\frac{81p^{8}\times 2^{5}\left(q^{5}\right)^{5}}{\left(4q^{3}\right)^{4}\times \left(3p^{3}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply $5$ and $5$ to get $25$.

$$\frac{81p^{8}\times 2^{5}q^{25}}{\left(4q^{3}\right)^{4}\times \left(3p^{3}\right)^{5}}$$

Calculate $2$ to the power of $5$ and get $32$.

$$\frac{81p^{8}\times 32q^{25}}{\left(4q^{3}\right)^{4}\times \left(3p^{3}\right)^{5}}$$

Multiply $81$ and $32$ to get $2592$.

$$\frac{2592p^{8}q^{25}}{\left(4q^{3}\right)^{4}\times \left(3p^{3}\right)^{5}}$$

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

$$\frac{2592p^{8}q^{25}}{4^{4}\left(q^{3}\right)^{4}\times \left(3p^{3}\right)^{5}}$$

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

$$\frac{2592p^{8}q^{25}}{4^{4}q^{12}\times \left(3p^{3}\right)^{5}}$$

Calculate $4$ to the power of $4$ and get $256$.

$$\frac{2592p^{8}q^{25}}{256q^{12}\times \left(3p^{3}\right)^{5}}$$

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

$$\frac{2592p^{8}q^{25}}{256q^{12}\times 3^{5}\left(p^{3}\right)^{5}}$$

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

$$\frac{2592p^{8}q^{25}}{256q^{12}\times 3^{5}p^{15}}$$

Calculate $3$ to the power of $5$ and get $243$.

$$\frac{2592p^{8}q^{25}}{256q^{12}\times 243p^{15}}$$

Multiply $256$ and $243$ to get $62208$.

$$\frac{2592p^{8}q^{25}}{62208q^{12}p^{15}}$$

Cancel out $2592p^{8}q^{12}$ in both numerator and denominator.

$$\frac{q^{13}}{24p^{7}}$$