Solve ((3x ^ 3 * y ^ - 2)/(4x ^ 5 * y ^ - 3 * y ^ 0)) ^ - 3 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

$$( \frac { 3 x ^ { 3 } y ^ { - 2 } } { 4 x ^ { 5 } y ^ { - 3 } y ^ { 0 } } ) ^ { - 3 }$$

Evaluate

$\frac{64x^{6}}{27y^{3}}$

Solution Steps

To multiply powers of the same base, add their exponents. Add $-3$ and $0$ to get $-3$.

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

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

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

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

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

Calculate $y$ to the power of $1$ and get $y$.

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

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

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

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

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

Calculate $3$ to the power of $-3$ and get $\frac{1}{27}$.

$$\frac{\frac{1}{27}y^{-3}}{\left(4x^{2}\right)^{-3}}$$

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

$$\frac{\frac{1}{27}y^{-3}}{4^{-3}\left(x^{2}\right)^{-3}}$$

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

$$\frac{\frac{1}{27}y^{-3}}{4^{-3}x^{-6}}$$

Calculate $4$ to the power of $-3$ and get $\frac{1}{64}$.

$$\frac{\frac{1}{27}y^{-3}}{\frac{1}{64}x^{-6}}$$

Expand

$\frac{64x^{6}}{27y^{3}}$

Solution Steps

To multiply powers of the same base, add their exponents. Add $-3$ and $0$ to get $-3$.

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

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

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

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

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

Calculate $y$ to the power of $1$ and get $y$.

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

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

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

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

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

Calculate $3$ to the power of $-3$ and get $\frac{1}{27}$.

$$\frac{\frac{1}{27}y^{-3}}{\left(4x^{2}\right)^{-3}}$$

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

$$\frac{\frac{1}{27}y^{-3}}{4^{-3}\left(x^{2}\right)^{-3}}$$

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

$$\frac{\frac{1}{27}y^{-3}}{4^{-3}x^{-6}}$$

Calculate $4$ to the power of $-3$ and get $\frac{1}{64}$.

$$\frac{\frac{1}{27}y^{-3}}{\frac{1}{64}x^{-6}}$$