Solve (f^{3}g^2)^3*f^-9g^4

$$( f ^ { 3 } g ^ { 2 } ) ^ { 3 } \times f ^ { - 9 } g ^ { 4 }$$

Evaluate

$$g^{10}$$

Solution Steps

Expand \left(f^{3}g^{2}\right)^{3}.

$$\left(f^{3}\right)^{3}\left(g^{2}\right)^{3}f^{-9}g^{4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$f^{9}\left(g^{2}\right)^{3}f^{-9}g^{4}$$

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

$$f^{9}g^{6}f^{-9}g^{4}$$

Multiply f^{9} and f^{-9} to get 1.

$$g^{6}g^{4}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$g^{10}$$

Expand

$$g^{10}$$

Solution Steps

Expand \left(f^{3}g^{2}\right)^{3}.

$$\left(f^{3}\right)^{3}\left(g^{2}\right)^{3}f^{-9}g^{4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$f^{9}\left(g^{2}\right)^{3}f^{-9}g^{4}$$

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

$$f^{9}g^{6}f^{-9}g^{4}$$

Multiply f^{9} and f^{-9} to get 1.

$$g^{6}g^{4}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$g^{10}$$