Solve (((a ^ 4 * y ^ - 2)/(b ^ 4 * x ^ - 1)) ^ - 3) / (((a ^ - 2 * b ^ 4)/(x ^ - 3 * y ^ 4)) ^ 9) = | 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

$$(\frac{a^{4}y^{-2}}{b^{4}x^{-1}})^{-3}\div(\frac{a^{-2}b^{4}}{x^{-3}y^{4}})^{9}=$$

Evaluate

$\frac{a^{6}y^{42}}{b^{24}x^{30}}$

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.

$$\frac{\frac{\left(a^{4}y^{-2}\right)^{-3}}{\left(b^{4}x^{-1}\right)^{-3}}}{\left(\frac{a^{-2}b^{4}}{x^{-3}y^{4}}\right)^{9}}$$

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

$$\frac{\frac{\left(a^{4}y^{-2}\right)^{-3}}{\left(b^{4}x^{-1}\right)^{-3}}}{\frac{\left(a^{-2}b^{4}\right)^{9}}{\left(x^{-3}y^{4}\right)^{9}}}$$

Divide $\frac{\left(a^{4}y^{-2}\right)^{-3}}{\left(b^{4}x^{-1}\right)^{-3}}$ by $\frac{\left(a^{-2}b^{4}\right)^{9}}{\left(x^{-3}y^{4}\right)^{9}}$ by multiplying $\frac{\left(a^{4}y^{-2}\right)^{-3}}{\left(b^{4}x^{-1}\right)^{-3}}$ by the reciprocal of $\frac{\left(a^{-2}b^{4}\right)^{9}}{\left(x^{-3}y^{4}\right)^{9}}$.

$$\frac{\left(a^{4}y^{-2}\right)^{-3}\left(x^{-3}y^{4}\right)^{9}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

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

$$\frac{\left(a^{4}\right)^{-3}\left(y^{-2}\right)^{-3}\left(x^{-3}y^{4}\right)^{9}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

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

$$\frac{a^{-12}\left(y^{-2}\right)^{-3}\left(x^{-3}y^{4}\right)^{9}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

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

$$\frac{a^{-12}y^{6}\left(x^{-3}y^{4}\right)^{9}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

Expand $\left(x^{-3}y^{4}\right)^{9}$.

$$\frac{a^{-12}y^{6}\left(x^{-3}\right)^{9}\left(y^{4}\right)^{9}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

To raise a power to another power, multiply the exponents. Multiply $-3$ and $9$ to get $-27$.

$$\frac{a^{-12}y^{6}x^{-27}\left(y^{4}\right)^{9}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

To raise a power to another power, multiply the exponents. Multiply $4$ and $9$ to get $36$.

$$\frac{a^{-12}y^{6}x^{-27}y^{36}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

To multiply powers of the same base, add their exponents. Add $6$ and $36$ to get $42$.

$$\frac{a^{-12}y^{42}x^{-27}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

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

$$\frac{a^{-12}y^{42}x^{-27}}{\left(b^{4}\right)^{-3}\left(x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

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

$$\frac{a^{-12}y^{42}x^{-27}}{b^{-12}\left(x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

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

$$\frac{a^{-12}y^{42}x^{-27}}{b^{-12}x^{3}\left(a^{-2}b^{4}\right)^{9}}$$

Expand $\left(a^{-2}b^{4}\right)^{9}$.

$$\frac{a^{-12}y^{42}x^{-27}}{b^{-12}x^{3}\left(a^{-2}\right)^{9}\left(b^{4}\right)^{9}}$$

To raise a power to another power, multiply the exponents. Multiply $-2$ and $9$ to get $-18$.

$$\frac{a^{-12}y^{42}x^{-27}}{b^{-12}x^{3}a^{-18}\left(b^{4}\right)^{9}}$$

To raise a power to another power, multiply the exponents. Multiply $4$ and $9$ to get $36$.

$$\frac{a^{-12}y^{42}x^{-27}}{b^{-12}x^{3}a^{-18}b^{36}}$$

To multiply powers of the same base, add their exponents. Add $-12$ and $36$ to get $24$.

$$\frac{a^{-12}y^{42}x^{-27}}{b^{24}x^{3}a^{-18}}$$

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

$$\frac{x^{-27}a^{6}y^{42}}{x^{3}b^{24}}$$

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

$$\frac{a^{6}y^{42}}{b^{24}x^{30}}$$

Expand

$\frac{a^{6}y^{42}}{b^{24}x^{30}}$

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.

$$\frac{\frac{\left(a^{4}y^{-2}\right)^{-3}}{\left(b^{4}x^{-1}\right)^{-3}}}{\left(\frac{a^{-2}b^{4}}{x^{-3}y^{4}}\right)^{9}}$$

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

$$\frac{\frac{\left(a^{4}y^{-2}\right)^{-3}}{\left(b^{4}x^{-1}\right)^{-3}}}{\frac{\left(a^{-2}b^{4}\right)^{9}}{\left(x^{-3}y^{4}\right)^{9}}}$$

Divide $\frac{\left(a^{4}y^{-2}\right)^{-3}}{\left(b^{4}x^{-1}\right)^{-3}}$ by $\frac{\left(a^{-2}b^{4}\right)^{9}}{\left(x^{-3}y^{4}\right)^{9}}$ by multiplying $\frac{\left(a^{4}y^{-2}\right)^{-3}}{\left(b^{4}x^{-1}\right)^{-3}}$ by the reciprocal of $\frac{\left(a^{-2}b^{4}\right)^{9}}{\left(x^{-3}y^{4}\right)^{9}}$.

$$\frac{\left(a^{4}y^{-2}\right)^{-3}\left(x^{-3}y^{4}\right)^{9}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

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

$$\frac{\left(a^{4}\right)^{-3}\left(y^{-2}\right)^{-3}\left(x^{-3}y^{4}\right)^{9}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

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

$$\frac{a^{-12}\left(y^{-2}\right)^{-3}\left(x^{-3}y^{4}\right)^{9}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

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

$$\frac{a^{-12}y^{6}\left(x^{-3}y^{4}\right)^{9}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

Expand $\left(x^{-3}y^{4}\right)^{9}$.

$$\frac{a^{-12}y^{6}\left(x^{-3}\right)^{9}\left(y^{4}\right)^{9}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

To raise a power to another power, multiply the exponents. Multiply $-3$ and $9$ to get $-27$.

$$\frac{a^{-12}y^{6}x^{-27}\left(y^{4}\right)^{9}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

To raise a power to another power, multiply the exponents. Multiply $4$ and $9$ to get $36$.

$$\frac{a^{-12}y^{6}x^{-27}y^{36}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

To multiply powers of the same base, add their exponents. Add $6$ and $36$ to get $42$.

$$\frac{a^{-12}y^{42}x^{-27}}{\left(b^{4}x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

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

$$\frac{a^{-12}y^{42}x^{-27}}{\left(b^{4}\right)^{-3}\left(x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

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

$$\frac{a^{-12}y^{42}x^{-27}}{b^{-12}\left(x^{-1}\right)^{-3}\left(a^{-2}b^{4}\right)^{9}}$$

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

$$\frac{a^{-12}y^{42}x^{-27}}{b^{-12}x^{3}\left(a^{-2}b^{4}\right)^{9}}$$

Expand $\left(a^{-2}b^{4}\right)^{9}$.

$$\frac{a^{-12}y^{42}x^{-27}}{b^{-12}x^{3}\left(a^{-2}\right)^{9}\left(b^{4}\right)^{9}}$$

To raise a power to another power, multiply the exponents. Multiply $-2$ and $9$ to get $-18$.

$$\frac{a^{-12}y^{42}x^{-27}}{b^{-12}x^{3}a^{-18}\left(b^{4}\right)^{9}}$$

To raise a power to another power, multiply the exponents. Multiply $4$ and $9$ to get $36$.

$$\frac{a^{-12}y^{42}x^{-27}}{b^{-12}x^{3}a^{-18}b^{36}}$$

To multiply powers of the same base, add their exponents. Add $-12$ and $36$ to get $24$.

$$\frac{a^{-12}y^{42}x^{-27}}{b^{24}x^{3}a^{-18}}$$

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

$$\frac{x^{-27}a^{6}y^{42}}{x^{3}b^{24}}$$

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

$$\frac{a^{6}y^{42}}{b^{24}x^{30}}$$