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

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

Evaluate

$\frac{10b^{5}}{a^{9}}$

Solution Steps

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

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

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

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

Divide $\frac{\left(4a^{3}\right)^{2}}{\left(5b^{2}\right)^{2}}$ by $\frac{\left(2a^{5}\right)^{3}}{\left(5b^{3}\right)^{3}}$ by multiplying $\frac{\left(4a^{3}\right)^{2}}{\left(5b^{2}\right)^{2}}$ by the reciprocal of $\frac{\left(2a^{5}\right)^{3}}{\left(5b^{3}\right)^{3}}$.

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

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

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

To raise a power to another power, multiply the exponents. Multiply $3$ and $2$ to get $6$.

$$\frac{4^{2}a^{6}\times \left(5b^{3}\right)^{3}}{\left(5b^{2}\right)^{2}\times \left(2a^{5}\right)^{3}}$$

Calculate $4$ to the power of $2$ and get $16$.

$$\frac{16a^{6}\times \left(5b^{3}\right)^{3}}{\left(5b^{2}\right)^{2}\times \left(2a^{5}\right)^{3}}$$

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

$$\frac{16a^{6}\times 5^{3}\left(b^{3}\right)^{3}}{\left(5b^{2}\right)^{2}\times \left(2a^{5}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply $3$ and $3$ to get $9$.

$$\frac{16a^{6}\times 5^{3}b^{9}}{\left(5b^{2}\right)^{2}\times \left(2a^{5}\right)^{3}}$$

Calculate $5$ to the power of $3$ and get $125$.

$$\frac{16a^{6}\times 125b^{9}}{\left(5b^{2}\right)^{2}\times \left(2a^{5}\right)^{3}}$$

Multiply $16$ and $125$ to get $2000$.

$$\frac{2000a^{6}b^{9}}{\left(5b^{2}\right)^{2}\times \left(2a^{5}\right)^{3}}$$

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

$$\frac{2000a^{6}b^{9}}{5^{2}\left(b^{2}\right)^{2}\times \left(2a^{5}\right)^{3}}$$

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

$$\frac{2000a^{6}b^{9}}{5^{2}b^{4}\times \left(2a^{5}\right)^{3}}$$

Calculate $5$ to the power of $2$ and get $25$.

$$\frac{2000a^{6}b^{9}}{25b^{4}\times \left(2a^{5}\right)^{3}}$$

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

$$\frac{2000a^{6}b^{9}}{25b^{4}\times 2^{3}\left(a^{5}\right)^{3}}$$

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

$$\frac{2000a^{6}b^{9}}{25b^{4}\times 2^{3}a^{15}}$$

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

$$\frac{2000a^{6}b^{9}}{25b^{4}\times 8a^{15}}$$

Multiply $25$ and $8$ to get $200$.

$$\frac{2000a^{6}b^{9}}{200b^{4}a^{15}}$$

Cancel out $200b^{4}a^{6}$ in both numerator and denominator.

$$\frac{10b^{5}}{a^{9}}$$

Expand

$\frac{10b^{5}}{a^{9}}$

Solution Steps

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

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

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

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

Divide $\frac{\left(4a^{3}\right)^{2}}{\left(5b^{2}\right)^{2}}$ by $\frac{\left(2a^{5}\right)^{3}}{\left(5b^{3}\right)^{3}}$ by multiplying $\frac{\left(4a^{3}\right)^{2}}{\left(5b^{2}\right)^{2}}$ by the reciprocal of $\frac{\left(2a^{5}\right)^{3}}{\left(5b^{3}\right)^{3}}$.

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

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

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

To raise a power to another power, multiply the exponents. Multiply $3$ and $2$ to get $6$.

$$\frac{4^{2}a^{6}\times \left(5b^{3}\right)^{3}}{\left(5b^{2}\right)^{2}\times \left(2a^{5}\right)^{3}}$$

Calculate $4$ to the power of $2$ and get $16$.

$$\frac{16a^{6}\times \left(5b^{3}\right)^{3}}{\left(5b^{2}\right)^{2}\times \left(2a^{5}\right)^{3}}$$

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

$$\frac{16a^{6}\times 5^{3}\left(b^{3}\right)^{3}}{\left(5b^{2}\right)^{2}\times \left(2a^{5}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply $3$ and $3$ to get $9$.

$$\frac{16a^{6}\times 5^{3}b^{9}}{\left(5b^{2}\right)^{2}\times \left(2a^{5}\right)^{3}}$$

Calculate $5$ to the power of $3$ and get $125$.

$$\frac{16a^{6}\times 125b^{9}}{\left(5b^{2}\right)^{2}\times \left(2a^{5}\right)^{3}}$$

Multiply $16$ and $125$ to get $2000$.

$$\frac{2000a^{6}b^{9}}{\left(5b^{2}\right)^{2}\times \left(2a^{5}\right)^{3}}$$

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

$$\frac{2000a^{6}b^{9}}{5^{2}\left(b^{2}\right)^{2}\times \left(2a^{5}\right)^{3}}$$

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

$$\frac{2000a^{6}b^{9}}{5^{2}b^{4}\times \left(2a^{5}\right)^{3}}$$

Calculate $5$ to the power of $2$ and get $25$.

$$\frac{2000a^{6}b^{9}}{25b^{4}\times \left(2a^{5}\right)^{3}}$$

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

$$\frac{2000a^{6}b^{9}}{25b^{4}\times 2^{3}\left(a^{5}\right)^{3}}$$

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

$$\frac{2000a^{6}b^{9}}{25b^{4}\times 2^{3}a^{15}}$$

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

$$\frac{2000a^{6}b^{9}}{25b^{4}\times 8a^{15}}$$

Multiply $25$ and $8$ to get $200$.

$$\frac{2000a^{6}b^{9}}{200b^{4}a^{15}}$$

Cancel out $200b^{4}a^{6}$ in both numerator and denominator.

$$\frac{10b^{5}}{a^{9}}$$