Solve (a^2*b)^4*(a*b)^-2=

$$( a ^ { 2 } \cdot b ) ^ { 4 } \cdot ( a \cdot b ) ^ { - 2 } =$$

Evaluate

$$b^{2}a^{6}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(a^{2}b^{1}\right)^{4}\left(a^{1}b^{1}\right)^{-2}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(a^{2}\right)^{4}\left(b^{1}\right)^{4}\left(a^{1}\right)^{-2}\left(b^{1}\right)^{-2}$$

Use the Commutative Property of Multiplication.

$$\left(a^{2}\right)^{4}\left(a^{1}\right)^{-2}\left(b^{1}\right)^{4}\left(b^{1}\right)^{-2}$$

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

$$a^{2\times 4}a^{-2}b^{4}b^{-2}$$

Multiply 2 times 4.

$$a^{8}a^{-2}b^{4}b^{-2}$$

To multiply powers of the same base, add their exponents.

$$a^{8-2}b^{4-2}$$

Add the exponents 8 and -2.

$$a^{6}b^{4-2}$$

Add the exponents 4 and -2.

$$a^{6}b^{2}$$

Expand

$$b^{2}a^{6}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(a^{2}b^{1}\right)^{4}\left(a^{1}b^{1}\right)^{-2}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(a^{2}\right)^{4}\left(b^{1}\right)^{4}\left(a^{1}\right)^{-2}\left(b^{1}\right)^{-2}$$

Use the Commutative Property of Multiplication.

$$\left(a^{2}\right)^{4}\left(a^{1}\right)^{-2}\left(b^{1}\right)^{4}\left(b^{1}\right)^{-2}$$

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

$$a^{2\times 4}a^{-2}b^{4}b^{-2}$$

Multiply 2 times 4.

$$a^{8}a^{-2}b^{4}b^{-2}$$

To multiply powers of the same base, add their exponents.

$$a^{8-2}b^{4-2}$$

Add the exponents 8 and -2.

$$a^{6}b^{4-2}$$

Add the exponents 4 and -2.

$$a^{6}b^{2}$$