Solve (5)x^{4}*x^{3}*x^5+(x^7)^3(x)^4

$$( 5 ) x ^ { 4 } \cdot x ^ { 3 } \cdot x ^ { 5 } + ( x ^ { 7 } ) ^ { 3 } ( x ) ^ { 4 }$$

Evaluate

$$x^{12}\left(x^{13}+5\right)$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$5x^{7}x^{5}+\left(x^{7}\right)^{3}x^{4}$$

To multiply powers of the same base, add their exponents. Add 7 and 5 to get 12.

$$5x^{12}+\left(x^{7}\right)^{3}x^{4}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$5x^{12}+x^{21}x^{4}$$

To multiply powers of the same base, add their exponents. Add 21 and 4 to get 25.

$$5x^{12}+x^{25}$$

Factor

$$x^{12}\left(x^{13}+5\right)$$

Solution Steps

Factor out common term x^{4} by using distributive property.

$$x^{4}\left(5x^{3}x^{5}+\left(x^{7}\right)^{3}\right)$$

Consider 5x^{3}x^{5}+\left(x^{7}\right)^{3}. Simplify.

$$x^{21}+5x^{8}$$

Factor out x^{8}.

$$x^{8}\left(x^{13}+5\right)$$

Rewrite the complete factored expression.

$$x^{4}\left(x^{13}+5\right)x^{8}$$