Solve (((- 2x ^ 2 * y ^ 3)/(a ^ 2)) ^ 2) / (((2a ^ 2 * y ^ 2)/(x ^ - 2)) ^ 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

$$(\frac{-2x^{2}y^{3}}{a^{2}})^{2}\div(\frac{2a^{2}y^{2}}{x^{-2}})^{3}$$

Evaluate

$\frac{1}{2x^{2}a^{10}}$

Solution Steps

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

$$\frac{\frac{\left(-2x^{2}y^{3}\right)^{2}}{\left(a^{2}\right)^{2}}}{\left(\frac{2a^{2}y^{2}}{x^{-2}}\right)^{3}}$$

To raise $\frac{2a^{2}y^{2}}{x^{-2}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{\left(-2x^{2}y^{3}\right)^{2}}{\left(a^{2}\right)^{2}}}{\frac{\left(2a^{2}y^{2}\right)^{3}}{\left(x^{-2}\right)^{3}}}$$

Divide $\frac{\left(-2x^{2}y^{3}\right)^{2}}{\left(a^{2}\right)^{2}}$ by $\frac{\left(2a^{2}y^{2}\right)^{3}}{\left(x^{-2}\right)^{3}}$ by multiplying $\frac{\left(-2x^{2}y^{3}\right)^{2}}{\left(a^{2}\right)^{2}}$ by the reciprocal of $\frac{\left(2a^{2}y^{2}\right)^{3}}{\left(x^{-2}\right)^{3}}$.

$$\frac{\left(-2x^{2}y^{3}\right)^{2}\left(x^{-2}\right)^{3}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{3}}$$

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

$$\frac{\left(-2x^{2}y^{3}\right)^{2}x^{-6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{3}}$$

Expand $\left(-2x^{2}y^{3}\right)^{2}$.

$$\frac{\left(-2\right)^{2}\left(x^{2}\right)^{2}\left(y^{3}\right)^{2}x^{-6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{3}}$$

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

$$\frac{\left(-2\right)^{2}x^{4}\left(y^{3}\right)^{2}x^{-6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{3}}$$

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

$$\frac{\left(-2\right)^{2}x^{4}y^{6}x^{-6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{3}}$$

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

$$\frac{4x^{4}y^{6}x^{-6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add $4$ and $-6$ to get $-2$.

$$\frac{4x^{-2}y^{6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{3}}$$

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

$$\frac{4x^{-2}y^{6}}{a^{4}\times \left(2a^{2}y^{2}\right)^{3}}$$

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

$$\frac{4x^{-2}y^{6}}{a^{4}\times 2^{3}\left(a^{2}\right)^{3}\left(y^{2}\right)^{3}}$$

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

$$\frac{4x^{-2}y^{6}}{a^{4}\times 2^{3}a^{6}\left(y^{2}\right)^{3}}$$

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

$$\frac{4x^{-2}y^{6}}{a^{4}\times 2^{3}a^{6}y^{6}}$$

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

$$\frac{4x^{-2}y^{6}}{a^{4}\times 8a^{6}y^{6}}$$

To multiply powers of the same base, add their exponents. Add $4$ and $6$ to get $10$.

$$\frac{4x^{-2}y^{6}}{a^{10}\times 8y^{6}}$$

Cancel out $4y^{6}$ in both numerator and denominator.

$$\frac{x^{-2}}{2a^{10}}$$

Expand

$\frac{1}{2x^{2}a^{10}}$

Solution Steps

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

$$\frac{\frac{\left(-2x^{2}y^{3}\right)^{2}}{\left(a^{2}\right)^{2}}}{\left(\frac{2a^{2}y^{2}}{x^{-2}}\right)^{3}}$$

To raise $\frac{2a^{2}y^{2}}{x^{-2}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{\left(-2x^{2}y^{3}\right)^{2}}{\left(a^{2}\right)^{2}}}{\frac{\left(2a^{2}y^{2}\right)^{3}}{\left(x^{-2}\right)^{3}}}$$

Divide $\frac{\left(-2x^{2}y^{3}\right)^{2}}{\left(a^{2}\right)^{2}}$ by $\frac{\left(2a^{2}y^{2}\right)^{3}}{\left(x^{-2}\right)^{3}}$ by multiplying $\frac{\left(-2x^{2}y^{3}\right)^{2}}{\left(a^{2}\right)^{2}}$ by the reciprocal of $\frac{\left(2a^{2}y^{2}\right)^{3}}{\left(x^{-2}\right)^{3}}$.

$$\frac{\left(-2x^{2}y^{3}\right)^{2}\left(x^{-2}\right)^{3}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{3}}$$

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

$$\frac{\left(-2x^{2}y^{3}\right)^{2}x^{-6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{3}}$$

Expand $\left(-2x^{2}y^{3}\right)^{2}$.

$$\frac{\left(-2\right)^{2}\left(x^{2}\right)^{2}\left(y^{3}\right)^{2}x^{-6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{3}}$$

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

$$\frac{\left(-2\right)^{2}x^{4}\left(y^{3}\right)^{2}x^{-6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{3}}$$

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

$$\frac{\left(-2\right)^{2}x^{4}y^{6}x^{-6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{3}}$$

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

$$\frac{4x^{4}y^{6}x^{-6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add $4$ and $-6$ to get $-2$.

$$\frac{4x^{-2}y^{6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{3}}$$

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

$$\frac{4x^{-2}y^{6}}{a^{4}\times \left(2a^{2}y^{2}\right)^{3}}$$

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

$$\frac{4x^{-2}y^{6}}{a^{4}\times 2^{3}\left(a^{2}\right)^{3}\left(y^{2}\right)^{3}}$$

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

$$\frac{4x^{-2}y^{6}}{a^{4}\times 2^{3}a^{6}\left(y^{2}\right)^{3}}$$

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

$$\frac{4x^{-2}y^{6}}{a^{4}\times 2^{3}a^{6}y^{6}}$$

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

$$\frac{4x^{-2}y^{6}}{a^{4}\times 8a^{6}y^{6}}$$

To multiply powers of the same base, add their exponents. Add $4$ and $6$ to get $10$.

$$\frac{4x^{-2}y^{6}}{a^{10}\times 8y^{6}}$$

Cancel out $4y^{6}$ in both numerator and denominator.

$$\frac{x^{-2}}{2a^{10}}$$