Solve (4x ^ 2 * y ^ 3) ^ 3; (3x ^ 3 * y ^ 3) ^ 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

$$(\underline{4x^{2}y^{3}})^{3}; (3x^{3}y^{3})^{3}$$

Evaluate

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

Solution Steps

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

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

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

$$\frac{4^{3}x^{6}\left(y^{3}\right)^{3}}{\left(3x^{3}y^{3}\right)^{3}}$$

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

$$\frac{4^{3}x^{6}y^{9}}{\left(3x^{3}y^{3}\right)^{3}}$$

Calculate $4$ to the power of $3$ and get $64$.

$$\frac{64x^{6}y^{9}}{\left(3x^{3}y^{3}\right)^{3}}$$

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

$$\frac{64x^{6}y^{9}}{3^{3}\left(x^{3}\right)^{3}\left(y^{3}\right)^{3}}$$

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

$$\frac{64x^{6}y^{9}}{3^{3}x^{9}\left(y^{3}\right)^{3}}$$

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

$$\frac{64x^{6}y^{9}}{3^{3}x^{9}y^{9}}$$

Calculate $3$ to the power of $3$ and get $27$.

$$\frac{64x^{6}y^{9}}{27x^{9}y^{9}}$$

Cancel out $x^{6}y^{9}$ in both numerator and denominator.

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

Expand

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

Solution Steps

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

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

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

$$\frac{4^{3}x^{6}\left(y^{3}\right)^{3}}{\left(3x^{3}y^{3}\right)^{3}}$$

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

$$\frac{4^{3}x^{6}y^{9}}{\left(3x^{3}y^{3}\right)^{3}}$$

Calculate $4$ to the power of $3$ and get $64$.

$$\frac{64x^{6}y^{9}}{\left(3x^{3}y^{3}\right)^{3}}$$

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

$$\frac{64x^{6}y^{9}}{3^{3}\left(x^{3}\right)^{3}\left(y^{3}\right)^{3}}$$

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

$$\frac{64x^{6}y^{9}}{3^{3}x^{9}\left(y^{3}\right)^{3}}$$

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

$$\frac{64x^{6}y^{9}}{3^{3}x^{9}y^{9}}$$

Calculate $3$ to the power of $3$ and get $27$.

$$\frac{64x^{6}y^{9}}{27x^{9}y^{9}}$$

Cancel out $x^{6}y^{9}$ in both numerator and denominator.

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