Solve (x^2)^5*(-x)^5

$$( x ^ { 2 } ) ^ { 5 } \cdot ( - x ) ^ { 5 }$$

Evaluate

$$-x^{15}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(x^{2}\right)^{5}\left(-x^{1}\right)^{5}$$

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

$$1^{5}\left(x^{2}\right)^{5}\left(-1\right)\left(x^{1}\right)^{5}$$

Use the Commutative Property of Multiplication.

$$1^{5}\left(-1\right)\left(x^{2}\right)^{5}\left(x^{1}\right)^{5}$$

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

$$1^{5}\left(-1\right)x^{2\times 5}x^{5}$$

Multiply 2 times 5.

$$1^{5}\left(-1\right)x^{10}x^{5}$$

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

$$1^{5}\left(-1\right)x^{10+5}$$

Add the exponents 10 and 5.

$$1^{5}\left(-1\right)x^{15}$$

Raise -1 to the power 5.

$$-x^{15}$$

Expand

$$-x^{15}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(x^{2}\right)^{5}\left(-x^{1}\right)^{5}$$

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

$$1^{5}\left(x^{2}\right)^{5}\left(-1\right)\left(x^{1}\right)^{5}$$

Use the Commutative Property of Multiplication.

$$1^{5}\left(-1\right)\left(x^{2}\right)^{5}\left(x^{1}\right)^{5}$$

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

$$1^{5}\left(-1\right)x^{2\times 5}x^{5}$$

Multiply 2 times 5.

$$1^{5}\left(-1\right)x^{10}x^{5}$$

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

$$1^{5}\left(-1\right)x^{10+5}$$

Add the exponents 10 and 5.

$$1^{5}\left(-1\right)x^{15}$$

Raise -1 to the power 5.

$$-x^{15}$$