Solve (-a^5)^4*(-a^4)^5

$$( - a ^ { 5 } ) ^ { 4 } \cdot ( - a ^ { 4 } ) ^ { 5 }$$

Evaluate

$$-a^{40}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-a^{5}\right)^{4}\left(-a^{4}\right)^{5}$$

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

$$\left(a^{5}\right)^{4}\left(-1\right)\left(a^{4}\right)^{5}$$

Use the Commutative Property of Multiplication.

$$-\left(a^{5}\right)^{4}\left(a^{4}\right)^{5}$$

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

$$-a^{5\times 4}a^{4\times 5}$$

Multiply 5 times 4.

$$-a^{20}a^{4\times 5}$$

Multiply 4 times 5.

$$-a^{20}a^{20}$$

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

$$-a^{20+20}$$

Add the exponents 20 and 20.

$$-a^{40}$$

Expand

$$-a^{40}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-a^{5}\right)^{4}\left(-a^{4}\right)^{5}$$

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

$$\left(a^{5}\right)^{4}\left(-1\right)\left(a^{4}\right)^{5}$$

Use the Commutative Property of Multiplication.

$$-\left(a^{5}\right)^{4}\left(a^{4}\right)^{5}$$

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

$$-a^{5\times 4}a^{4\times 5}$$

Multiply 5 times 4.

$$-a^{20}a^{4\times 5}$$

Multiply 4 times 5.

$$-a^{20}a^{20}$$

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

$$-a^{20+20}$$

Add the exponents 20 and 20.

$$-a^{40}$$