Solve (g^7h)^6*(gh^9)^8

$$( g ^ { 7 } h ) ^ { 6 } \times ( g h ^ { 9 } ) ^ { 8 }$$

Evaluate

$$g^{50}h^{78}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(g^{7}h^{1}\right)^{6}\left(g^{1}h^{9}\right)^{8}$$

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

$$\left(g^{7}\right)^{6}\left(h^{1}\right)^{6}\left(g^{1}\right)^{8}\left(h^{9}\right)^{8}$$

Use the Commutative Property of Multiplication.

$$\left(g^{7}\right)^{6}\left(g^{1}\right)^{8}\left(h^{1}\right)^{6}\left(h^{9}\right)^{8}$$

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

$$g^{7\times 6}g^{8}h^{6}h^{9\times 8}$$

Multiply 7 times 6.

$$g^{42}g^{8}h^{6}h^{9\times 8}$$

Multiply 9 times 8.

$$g^{42}g^{8}h^{6}h^{72}$$

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

$$g^{42+8}h^{6+72}$$

Add the exponents 42 and 8.

$$g^{50}h^{6+72}$$

Add the exponents 6 and 72.

$$g^{50}h^{78}$$

Expand

$$g^{50}h^{78}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(g^{7}h^{1}\right)^{6}\left(g^{1}h^{9}\right)^{8}$$

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

$$\left(g^{7}\right)^{6}\left(h^{1}\right)^{6}\left(g^{1}\right)^{8}\left(h^{9}\right)^{8}$$

Use the Commutative Property of Multiplication.

$$\left(g^{7}\right)^{6}\left(g^{1}\right)^{8}\left(h^{1}\right)^{6}\left(h^{9}\right)^{8}$$

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

$$g^{7\times 6}g^{8}h^{6}h^{9\times 8}$$

Multiply 7 times 6.

$$g^{42}g^{8}h^{6}h^{9\times 8}$$

Multiply 9 times 8.

$$g^{42}g^{8}h^{6}h^{72}$$

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

$$g^{42+8}h^{6+72}$$

Add the exponents 42 and 8.

$$g^{50}h^{6+72}$$

Add the exponents 6 and 72.

$$g^{50}h^{78}$$