Solve (((a ^ 4 * y ^ - 2)/(b ^ 4 * x ^ - 1)) ^ - 3) / (((a ^ 2 * b ^ 4)/(x ^ 5 * y ^ 2)) ^ 2) = | 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

$$(\frac{a^{4}y^{-2}}{b^{4}x^{-1}})^{-3}\div(\frac{a^{2}b^{4}}{x^{5}y^{2}})^{2}=$$

Evaluate

$\frac{b^{4}x^{7}y^{10}}{a^{16}}$

Solution Steps

To raise $\frac{a^{4}y^{-2}}{b^{4}x^{-1}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{\left(a^{4}y^{-2}\right)^{-3}}{\left(b^{4}x^{-1}\right)^{-3}}}{\left(\frac{a^{2}b^{4}}{x^{5}y^{2}}\right)^{2}}$$

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

$$\frac{\frac{\left(a^{4}y^{-2}\right)^{-3}}{\left(b^{4}x^{-1}\right)^{-3}}}{\frac{\left(a^{2}b^{4}\right)^{2}}{\left(x^{5}y^{2}\right)^{2}}}$$

Divide $\frac{\left(a^{4}y^{-2}\right)^{-3}}{\left(b^{4}x^{-1}\right)^{-3}}$ by $\frac{\left(a^{2}b^{4}\right)^{2}}{\left(x^{5}y^{2}\right)^{2}}$ by multiplying $\frac{\left(a^{4}y^{-2}\right)^{-3}}{\left(b^{4}x^{-1}\right)^{-3}}$ by the reciprocal of $\frac{\left(a^{2}b^{4}\right)^{2}}{\left(x^{5}y^{2}\right)^{2}}$.

$$\frac{\left(a^{4}y^{-2}\right)^{-3}\left(x^{5}y^{2}\right)^{2}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

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

$$\frac{\left(a^{4}\right)^{-3}\left(y^{-2}\right)^{-3}\left(x^{5}y^{2}\right)^{2}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

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

$$\frac{a^{-12}\left(y^{-2}\right)^{-3}\left(x^{5}y^{2}\right)^{2}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

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

$$\frac{a^{-12}y^{6}\left(x^{5}y^{2}\right)^{2}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

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

$$\frac{a^{-12}y^{6}\left(x^{5}\right)^{2}\left(y^{2}\right)^{2}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply $5$ and $2$ to get $10$.

$$\frac{a^{-12}y^{6}x^{10}\left(y^{2}\right)^{2}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

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

$$\frac{a^{-12}y^{6}x^{10}y^{4}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

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

$$\frac{a^{-12}y^{10}x^{10}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

Expand $\left(b^{4}x^{-1}\right)^{-3}$.

$$\frac{a^{-12}y^{10}x^{10}}{\left(b^{4}\right)^{-3}\left(x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

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

$$\frac{a^{-12}y^{10}x^{10}}{b^{-12}\left(x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply $-1$ and $-3$ to get $3$.

$$\frac{a^{-12}y^{10}x^{10}}{b^{-12}x^{3}\left(a^{2}b^{4}\right)^{2}}$$

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

$$\frac{a^{-12}y^{10}x^{10}}{b^{-12}x^{3}\left(a^{2}\right)^{2}\left(b^{4}\right)^{2}}$$

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

$$\frac{a^{-12}y^{10}x^{10}}{b^{-12}x^{3}a^{4}\left(b^{4}\right)^{2}}$$

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

$$\frac{a^{-12}y^{10}x^{10}}{b^{-12}x^{3}a^{4}b^{8}}$$

To multiply powers of the same base, add their exponents. Add $-12$ and $8$ to get $-4$.

$$\frac{a^{-12}y^{10}x^{10}}{b^{-4}x^{3}a^{4}}$$

Cancel out $x^{3}$ in both numerator and denominator.

$$\frac{a^{-12}x^{7}y^{10}}{b^{-4}a^{4}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{x^{7}y^{10}}{b^{-4}a^{16}}$$

Expand

$\frac{b^{4}x^{7}y^{10}}{a^{16}}$

Solution Steps

To raise $\frac{a^{4}y^{-2}}{b^{4}x^{-1}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{\left(a^{4}y^{-2}\right)^{-3}}{\left(b^{4}x^{-1}\right)^{-3}}}{\left(\frac{a^{2}b^{4}}{x^{5}y^{2}}\right)^{2}}$$

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

$$\frac{\frac{\left(a^{4}y^{-2}\right)^{-3}}{\left(b^{4}x^{-1}\right)^{-3}}}{\frac{\left(a^{2}b^{4}\right)^{2}}{\left(x^{5}y^{2}\right)^{2}}}$$

Divide $\frac{\left(a^{4}y^{-2}\right)^{-3}}{\left(b^{4}x^{-1}\right)^{-3}}$ by $\frac{\left(a^{2}b^{4}\right)^{2}}{\left(x^{5}y^{2}\right)^{2}}$ by multiplying $\frac{\left(a^{4}y^{-2}\right)^{-3}}{\left(b^{4}x^{-1}\right)^{-3}}$ by the reciprocal of $\frac{\left(a^{2}b^{4}\right)^{2}}{\left(x^{5}y^{2}\right)^{2}}$.

$$\frac{\left(a^{4}y^{-2}\right)^{-3}\left(x^{5}y^{2}\right)^{2}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

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

$$\frac{\left(a^{4}\right)^{-3}\left(y^{-2}\right)^{-3}\left(x^{5}y^{2}\right)^{2}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

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

$$\frac{a^{-12}\left(y^{-2}\right)^{-3}\left(x^{5}y^{2}\right)^{2}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

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

$$\frac{a^{-12}y^{6}\left(x^{5}y^{2}\right)^{2}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

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

$$\frac{a^{-12}y^{6}\left(x^{5}\right)^{2}\left(y^{2}\right)^{2}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply $5$ and $2$ to get $10$.

$$\frac{a^{-12}y^{6}x^{10}\left(y^{2}\right)^{2}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

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

$$\frac{a^{-12}y^{6}x^{10}y^{4}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

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

$$\frac{a^{-12}y^{10}x^{10}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

Expand $\left(b^{4}x^{-1}\right)^{-3}$.

$$\frac{a^{-12}y^{10}x^{10}}{\left(b^{4}\right)^{-3}\left(x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

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

$$\frac{a^{-12}y^{10}x^{10}}{b^{-12}\left(x^{-1}\right)^{-3}\left(a^{2}b^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply $-1$ and $-3$ to get $3$.

$$\frac{a^{-12}y^{10}x^{10}}{b^{-12}x^{3}\left(a^{2}b^{4}\right)^{2}}$$

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

$$\frac{a^{-12}y^{10}x^{10}}{b^{-12}x^{3}\left(a^{2}\right)^{2}\left(b^{4}\right)^{2}}$$

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

$$\frac{a^{-12}y^{10}x^{10}}{b^{-12}x^{3}a^{4}\left(b^{4}\right)^{2}}$$

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

$$\frac{a^{-12}y^{10}x^{10}}{b^{-12}x^{3}a^{4}b^{8}}$$

To multiply powers of the same base, add their exponents. Add $-12$ and $8$ to get $-4$.

$$\frac{a^{-12}y^{10}x^{10}}{b^{-4}x^{3}a^{4}}$$

Cancel out $x^{3}$ in both numerator and denominator.

$$\frac{a^{-12}x^{7}y^{10}}{b^{-4}a^{4}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{x^{7}y^{10}}{b^{-4}a^{16}}$$