Solve ច័ន្ទ អង្គារ ពុធ ព្រហ សុក្រ សៅរ៍ អាទិត្យ កាលបរិច្ឆេទ 000000 (((- 2x ^ 2 * y ^ 3)/(a ^ 2)) ^ 4) / (((2a ^ 2 * y ^ 2)/(x ^ - 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

$$( \frac { - 2 x ^ { 2 } z ^ { 3 } } { a ^ { 2 } } ) ^ { 2 } \div ( \frac { 2 a ^ { 2 } y ^ { 2 } } { x ^ { - 2 } } ) ^ { - 3 }$$

Evaluate

$32a^{2}x^{10}\left(yz\right)^{6}$

Solution Steps

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

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

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

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

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

$$\frac{\left(-2x^{2}z^{3}\right)^{2}\left(x^{-2}\right)^{-3}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{-3}}$$

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

$$\frac{\left(-2x^{2}z^{3}\right)^{2}x^{6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{-3}}$$

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

$$\frac{\left(-2\right)^{2}\left(x^{2}\right)^{2}\left(z^{3}\right)^{2}x^{6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $2$ to get $4$.

$$\frac{\left(-2\right)^{2}x^{4}\left(z^{3}\right)^{2}x^{6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{-3}}$$

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

$$\frac{\left(-2\right)^{2}x^{4}z^{6}x^{6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{-3}}$$

Calculate $-2$ to the power of $2$ and get $4$.

$$\frac{4x^{4}z^{6}x^{6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{-3}}$$

To multiply powers of the same base, add their exponents. Add $4$ and $6$ to get $10$.

$$\frac{4x^{10}z^{6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $2$ to get $4$.

$$\frac{4x^{10}z^{6}}{a^{4}\times \left(2a^{2}y^{2}\right)^{-3}}$$

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

$$\frac{4x^{10}z^{6}}{a^{4}\times 2^{-3}\left(a^{2}\right)^{-3}\left(y^{2}\right)^{-3}}$$

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

$$\frac{4x^{10}z^{6}}{a^{4}\times 2^{-3}a^{-6}\left(y^{2}\right)^{-3}}$$

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

$$\frac{4x^{10}z^{6}}{a^{4}\times 2^{-3}a^{-6}y^{-6}}$$

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

$$\frac{4x^{10}z^{6}}{a^{4}\times \frac{1}{8}a^{-6}y^{-6}}$$

To multiply powers of the same base, add their exponents. Add $4$ and $-6$ to get $-2$.

$$\frac{4x^{10}z^{6}}{a^{-2}\times \frac{1}{8}y^{-6}}$$

Expand

$32a^{2}x^{10}\left(yz\right)^{6}$

Solution Steps

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

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

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

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

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

$$\frac{\left(-2x^{2}z^{3}\right)^{2}\left(x^{-2}\right)^{-3}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{-3}}$$

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

$$\frac{\left(-2x^{2}z^{3}\right)^{2}x^{6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{-3}}$$

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

$$\frac{\left(-2\right)^{2}\left(x^{2}\right)^{2}\left(z^{3}\right)^{2}x^{6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $2$ to get $4$.

$$\frac{\left(-2\right)^{2}x^{4}\left(z^{3}\right)^{2}x^{6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{-3}}$$

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

$$\frac{\left(-2\right)^{2}x^{4}z^{6}x^{6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{-3}}$$

Calculate $-2$ to the power of $2$ and get $4$.

$$\frac{4x^{4}z^{6}x^{6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{-3}}$$

To multiply powers of the same base, add their exponents. Add $4$ and $6$ to get $10$.

$$\frac{4x^{10}z^{6}}{\left(a^{2}\right)^{2}\times \left(2a^{2}y^{2}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $2$ to get $4$.

$$\frac{4x^{10}z^{6}}{a^{4}\times \left(2a^{2}y^{2}\right)^{-3}}$$

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

$$\frac{4x^{10}z^{6}}{a^{4}\times 2^{-3}\left(a^{2}\right)^{-3}\left(y^{2}\right)^{-3}}$$

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

$$\frac{4x^{10}z^{6}}{a^{4}\times 2^{-3}a^{-6}\left(y^{2}\right)^{-3}}$$

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

$$\frac{4x^{10}z^{6}}{a^{4}\times 2^{-3}a^{-6}y^{-6}}$$

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

$$\frac{4x^{10}z^{6}}{a^{4}\times \frac{1}{8}a^{-6}y^{-6}}$$

To multiply powers of the same base, add their exponents. Add $4$ and $-6$ to get $-2$.

$$\frac{4x^{10}z^{6}}{a^{-2}\times \frac{1}{8}y^{-6}}$$