Solve {left(2a^34a^2/8left(a^-3right)^2right)}^2

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

Evaluate

$$a^{22}$$

Steps for Raising Power to Another Power

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\left(\frac{2a^{5}\times 4}{8\left(a^{-3}\right)^{2}}\right)^{2}$$

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

$$\left(\frac{2a^{5}\times 4}{8a^{-6}}\right)^{2}$$

Cancel out 2\times 4 in both numerator and denominator.

$$\left(\frac{a^{5}}{a^{-6}}\right)^{2}$$

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

$$\left(a^{11}\right)^{2}$$

To raise a power to another power, multiply the exponents.

$$a^{11\times 2}$$

Multiply 11 times 2.

$$a^{22}$$

Expand

$$a^{22}$$

Steps for Raising Power to Another Power

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\left(\frac{2a^{5}\times 4}{8\left(a^{-3}\right)^{2}}\right)^{2}$$

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

$$\left(\frac{2a^{5}\times 4}{8a^{-6}}\right)^{2}$$

Cancel out 2\times 4 in both numerator and denominator.

$$\left(\frac{a^{5}}{a^{-6}}\right)^{2}$$

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

$$\left(a^{11}\right)^{2}$$

To raise a power to another power, multiply the exponents.

$$a^{11\times 2}$$

Multiply 11 times 2.

$$a^{22}$$