Solve (3a^2)^2+(5b^2)^2

$$( 3 a ^ { 2 } ) ^ { 2 } + ( 5 b ^ { 2 } ) ^ { 2 }$$

Evaluate

$$9a^{4}+25b^{4}$$

Solution Steps

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

$$3^{2}\left(a^{2}\right)^{2}+\left(5b^{2}\right)^{2}$$

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

$$3^{2}a^{4}+\left(5b^{2}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9a^{4}+\left(5b^{2}\right)^{2}$$

Expand \left(5b^{2}\right)^{2}.

$$9a^{4}+5^{2}\left(b^{2}\right)^{2}$$

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

$$9a^{4}+5^{2}b^{4}$$

Calculate 5 to the power of 2 and get 25.

$$9a^{4}+25b^{4}$$

Expand

$$9a^{4}+25b^{4}$$

Solution Steps

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

$$3^{2}\left(a^{2}\right)^{2}+\left(5b^{2}\right)^{2}$$

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

$$3^{2}a^{4}+\left(5b^{2}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9a^{4}+\left(5b^{2}\right)^{2}$$

Expand \left(5b^{2}\right)^{2}.

$$9a^{4}+5^{2}\left(b^{2}\right)^{2}$$

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

$$9a^{4}+5^{2}b^{4}$$

Calculate 5 to the power of 2 and get 25.

$$9a^{4}+25b^{4}$$