Solve =( 2^ 2 a^ 2 y y^ 2 x^ 4 )^ 2 ( 2^ 3 x^ 4 b^ 2 a^ -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

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

Evaluate

$\frac{1}{32b^{6}\left(ay\right)^{2}x^{20}}$

Solution Steps

Cancel out $y$ in both numerator and denominator.

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

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

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

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

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

Calculate $2$ to the power of $3$ and get $8$.

$$\frac{\left(4a^{2}\right)^{2}}{\left(yx^{4}\right)^{2}}\times \left(\frac{8x^{4}b^{2}}{a^{-2}}\right)^{-3}$$

To raise $\frac{8x^{4}b^{2}}{a^{-2}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4a^{2}\right)^{2}}{\left(yx^{4}\right)^{2}}\times \frac{\left(8x^{4}b^{2}\right)^{-3}}{\left(a^{-2}\right)^{-3}}$$

Multiply $\frac{\left(4a^{2}\right)^{2}}{\left(yx^{4}\right)^{2}}$ times $\frac{\left(8x^{4}b^{2}\right)^{-3}}{\left(a^{-2}\right)^{-3}}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4a^{2}\right)^{2}\times \left(8x^{4}b^{2}\right)^{-3}}{\left(yx^{4}\right)^{2}\left(a^{-2}\right)^{-3}}$$

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

$$\frac{\left(4a^{2}\right)^{2}\times \left(8x^{4}b^{2}\right)^{-3}}{\left(yx^{4}\right)^{2}a^{6}}$$

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

$$\frac{4^{2}\left(a^{2}\right)^{2}\times \left(8x^{4}b^{2}\right)^{-3}}{\left(yx^{4}\right)^{2}a^{6}}$$

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

$$\frac{4^{2}a^{4}\times \left(8x^{4}b^{2}\right)^{-3}}{\left(yx^{4}\right)^{2}a^{6}}$$

Calculate $4$ to the power of $2$ and get $16$.

$$\frac{16a^{4}\times \left(8x^{4}b^{2}\right)^{-3}}{\left(yx^{4}\right)^{2}a^{6}}$$

Expand $\left(8x^{4}b^{2}\right)^{-3}$.

$$\frac{16a^{4}\times 8^{-3}\left(x^{4}\right)^{-3}\left(b^{2}\right)^{-3}}{\left(yx^{4}\right)^{2}a^{6}}$$

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

$$\frac{16a^{4}\times 8^{-3}x^{-12}\left(b^{2}\right)^{-3}}{\left(yx^{4}\right)^{2}a^{6}}$$

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

$$\frac{16a^{4}\times 8^{-3}x^{-12}b^{-6}}{\left(yx^{4}\right)^{2}a^{6}}$$

Calculate $8$ to the power of $-3$ and get $\frac{1}{512}$.

$$\frac{16a^{4}\times \frac{1}{512}x^{-12}b^{-6}}{\left(yx^{4}\right)^{2}a^{6}}$$

Multiply $16$ and $\frac{1}{512}$ to get $\frac{1}{32}$.

$$\frac{\frac{1}{32}a^{4}x^{-12}b^{-6}}{\left(yx^{4}\right)^{2}a^{6}}$$

Expand $\left(yx^{4}\right)^{2}$.

$$\frac{\frac{1}{32}a^{4}x^{-12}b^{-6}}{y^{2}\left(x^{4}\right)^{2}a^{6}}$$

To raise a power to another power, multiply the exponents. Multiply $4$ and $2$ to get $8$.

$$\frac{\frac{1}{32}a^{4}x^{-12}b^{-6}}{y^{2}x^{8}a^{6}}$$

Cancel out $a^{4}$ in both numerator and denominator.

$$\frac{\frac{1}{32}x^{-12}b^{-6}}{a^{2}y^{2}x^{8}}$$

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

$$\frac{\frac{1}{32}b^{-6}}{a^{2}y^{2}x^{20}}$$

Expand

$\frac{1}{32b^{6}\left(ay\right)^{2}x^{20}}$

Solution Steps

Cancel out $y$ in both numerator and denominator.

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

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

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

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

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

Calculate $2$ to the power of $3$ and get $8$.

$$\frac{\left(4a^{2}\right)^{2}}{\left(yx^{4}\right)^{2}}\times \left(\frac{8x^{4}b^{2}}{a^{-2}}\right)^{-3}$$

To raise $\frac{8x^{4}b^{2}}{a^{-2}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4a^{2}\right)^{2}}{\left(yx^{4}\right)^{2}}\times \frac{\left(8x^{4}b^{2}\right)^{-3}}{\left(a^{-2}\right)^{-3}}$$

Multiply $\frac{\left(4a^{2}\right)^{2}}{\left(yx^{4}\right)^{2}}$ times $\frac{\left(8x^{4}b^{2}\right)^{-3}}{\left(a^{-2}\right)^{-3}}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4a^{2}\right)^{2}\times \left(8x^{4}b^{2}\right)^{-3}}{\left(yx^{4}\right)^{2}\left(a^{-2}\right)^{-3}}$$

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

$$\frac{\left(4a^{2}\right)^{2}\times \left(8x^{4}b^{2}\right)^{-3}}{\left(yx^{4}\right)^{2}a^{6}}$$

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

$$\frac{4^{2}\left(a^{2}\right)^{2}\times \left(8x^{4}b^{2}\right)^{-3}}{\left(yx^{4}\right)^{2}a^{6}}$$

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

$$\frac{4^{2}a^{4}\times \left(8x^{4}b^{2}\right)^{-3}}{\left(yx^{4}\right)^{2}a^{6}}$$

Calculate $4$ to the power of $2$ and get $16$.

$$\frac{16a^{4}\times \left(8x^{4}b^{2}\right)^{-3}}{\left(yx^{4}\right)^{2}a^{6}}$$

Expand $\left(8x^{4}b^{2}\right)^{-3}$.

$$\frac{16a^{4}\times 8^{-3}\left(x^{4}\right)^{-3}\left(b^{2}\right)^{-3}}{\left(yx^{4}\right)^{2}a^{6}}$$

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

$$\frac{16a^{4}\times 8^{-3}x^{-12}\left(b^{2}\right)^{-3}}{\left(yx^{4}\right)^{2}a^{6}}$$

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

$$\frac{16a^{4}\times 8^{-3}x^{-12}b^{-6}}{\left(yx^{4}\right)^{2}a^{6}}$$

Calculate $8$ to the power of $-3$ and get $\frac{1}{512}$.

$$\frac{16a^{4}\times \frac{1}{512}x^{-12}b^{-6}}{\left(yx^{4}\right)^{2}a^{6}}$$

Multiply $16$ and $\frac{1}{512}$ to get $\frac{1}{32}$.

$$\frac{\frac{1}{32}a^{4}x^{-12}b^{-6}}{\left(yx^{4}\right)^{2}a^{6}}$$

Expand $\left(yx^{4}\right)^{2}$.

$$\frac{\frac{1}{32}a^{4}x^{-12}b^{-6}}{y^{2}\left(x^{4}\right)^{2}a^{6}}$$

To raise a power to another power, multiply the exponents. Multiply $4$ and $2$ to get $8$.

$$\frac{\frac{1}{32}a^{4}x^{-12}b^{-6}}{y^{2}x^{8}a^{6}}$$

Cancel out $a^{4}$ in both numerator and denominator.

$$\frac{\frac{1}{32}x^{-12}b^{-6}}{a^{2}y^{2}x^{8}}$$

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

$$\frac{\frac{1}{32}b^{-6}}{a^{2}y^{2}x^{20}}$$