Solve frac{(a^{2}b^{2})^{3}x(a^2sqrt{a})^2}{a^3b^2}=

$$\frac { ( a ^ { 2 } b ^ { 2 } ) ^ { 3 } x ( a ^ { 2 } \sqrt { a } ) ^ { 2 } } { a ^ { 3 } b ^ { 2 } } =$$

Evaluate

$$xb^{4}a^{8}$$

Solution Steps

Expand \left(a^{2}b^{2}\right)^{3}.

$$\frac{\left(a^{2}\right)^{3}\left(b^{2}\right)^{3}x\left(a^{2}\sqrt{a}\right)^{2}}{a^{3}b^{2}}$$

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

$$\frac{a^{6}\left(b^{2}\right)^{3}x\left(a^{2}\sqrt{a}\right)^{2}}{a^{3}b^{2}}$$

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

$$\frac{a^{6}b^{6}x\left(a^{2}\sqrt{a}\right)^{2}}{a^{3}b^{2}}$$

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

$$\frac{a^{6}b^{6}x\left(a^{2}\right)^{2}\left(\sqrt{a}\right)^{2}}{a^{3}b^{2}}$$

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

$$\frac{a^{6}b^{6}xa^{4}\left(\sqrt{a}\right)^{2}}{a^{3}b^{2}}$$

Calculate \sqrt{a} to the power of 2 and get a.

$$\frac{a^{6}b^{6}xa^{4}a}{a^{3}b^{2}}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{a^{6}b^{6}xa^{5}}{a^{3}b^{2}}$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$\frac{a^{11}b^{6}x}{a^{3}b^{2}}$$

Cancel out b^{2}a^{3} in both numerator and denominator.

$$xb^{4}a^{8}$$

Expand

$$xb^{4}a^{8}$$

Solution Steps

Expand \left(a^{2}b^{2}\right)^{3}.

$$\frac{\left(a^{2}\right)^{3}\left(b^{2}\right)^{3}x\left(a^{2}\sqrt{a}\right)^{2}}{a^{3}b^{2}}$$

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

$$\frac{a^{6}\left(b^{2}\right)^{3}x\left(a^{2}\sqrt{a}\right)^{2}}{a^{3}b^{2}}$$

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

$$\frac{a^{6}b^{6}x\left(a^{2}\sqrt{a}\right)^{2}}{a^{3}b^{2}}$$

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

$$\frac{a^{6}b^{6}x\left(a^{2}\right)^{2}\left(\sqrt{a}\right)^{2}}{a^{3}b^{2}}$$

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

$$\frac{a^{6}b^{6}xa^{4}\left(\sqrt{a}\right)^{2}}{a^{3}b^{2}}$$

Calculate \sqrt{a} to the power of 2 and get a.

$$\frac{a^{6}b^{6}xa^{4}a}{a^{3}b^{2}}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{a^{6}b^{6}xa^{5}}{a^{3}b^{2}}$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$\frac{a^{11}b^{6}x}{a^{3}b^{2}}$$

Cancel out b^{2}a^{3} in both numerator and denominator.

$$xb^{4}a^{8}$$