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

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

Evaluate

$\frac{I\left(by\right)^{8}}{x^{6}a^{10}}$

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.

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

Express $I\times \frac{\left(a^{4}y^{-2}\right)^{-3}}{\left(b^{4}x^{-1}\right)^{-3}}$ as a single fraction.

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

Calculate $\frac{a^{-2}b^{4}}{x^{-3}y^{2}}$ to the power of $1$ and get $\frac{a^{-2}b^{4}}{x^{-3}y^{2}}$.

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

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

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

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

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add $6$ and $2$ to get $8$.

$$\frac{Ia^{-12}y^{8}x^{-3}}{\left(b^{4}x^{-1}\right)^{-3}a^{-2}b^{4}}$$

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

$$\frac{Ia^{-12}y^{8}x^{-3}}{\left(b^{4}\right)^{-3}\left(x^{-1}\right)^{-3}a^{-2}b^{4}}$$

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

$$\frac{Ia^{-12}y^{8}x^{-3}}{b^{-12}\left(x^{-1}\right)^{-3}a^{-2}b^{4}}$$

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

$$\frac{Ia^{-12}y^{8}x^{-3}}{b^{-12}x^{3}a^{-2}b^{4}}$$

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

$$\frac{Ia^{-12}y^{8}x^{-3}}{b^{-8}x^{3}a^{-2}}$$

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

$$\frac{Iy^{8}}{b^{-8}x^{6}a^{10}}$$

Expand

$\frac{I\left(by\right)^{8}}{x^{6}a^{10}}$

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.

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

Express $I\times \frac{\left(a^{4}y^{-2}\right)^{-3}}{\left(b^{4}x^{-1}\right)^{-3}}$ as a single fraction.

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

Calculate $\frac{a^{-2}b^{4}}{x^{-3}y^{2}}$ to the power of $1$ and get $\frac{a^{-2}b^{4}}{x^{-3}y^{2}}$.

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

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

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

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

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add $6$ and $2$ to get $8$.

$$\frac{Ia^{-12}y^{8}x^{-3}}{\left(b^{4}x^{-1}\right)^{-3}a^{-2}b^{4}}$$

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

$$\frac{Ia^{-12}y^{8}x^{-3}}{\left(b^{4}\right)^{-3}\left(x^{-1}\right)^{-3}a^{-2}b^{4}}$$

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

$$\frac{Ia^{-12}y^{8}x^{-3}}{b^{-12}\left(x^{-1}\right)^{-3}a^{-2}b^{4}}$$

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

$$\frac{Ia^{-12}y^{8}x^{-3}}{b^{-12}x^{3}a^{-2}b^{4}}$$

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

$$\frac{Ia^{-12}y^{8}x^{-3}}{b^{-8}x^{3}a^{-2}}$$

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

$$\frac{Iy^{8}}{b^{-8}x^{6}a^{10}}$$