Solve ((2x ^ - 1 * y)/(x ^ - 3 * y ^ - 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

$$(\frac{2x^{-1}y}{x^{-3}y^{-2}})^{-3}$$

Evaluate

$\frac{1}{8x^{6}y^{9}}$

Solution Steps

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

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

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

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

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

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

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

$$2^{-3}x^{-6}y^{-9}$$

Calculate $2$ to the power of $-3$ and get $\frac{1}{8}$.

$$\frac{1}{8}x^{-6}y^{-9}$$

Expand

$\frac{1}{8x^{6}y^{9}}$

Solution Steps

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

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

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

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

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

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

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

$$2^{-3}x^{-6}y^{-9}$$

Calculate $2$ to the power of $-3$ and get $\frac{1}{8}$.

$$\frac{1}{8}x^{-6}y^{-9}$$