Solve (-5a^2)^3*a^5

$$( - 5 a ^ { 2 } ) ^ { 3 } \cdot a ^ { 5 }$$

Evaluate

$$-125a^{11}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-5a^{2}\right)^{3}\left(a^{1}\right)^{5}$$

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

$$\left(-5\right)^{3}\left(a^{2}\right)^{3}\times 1^{5}\left(a^{1}\right)^{5}$$

Use the Commutative Property of Multiplication.

$$\left(-5\right)^{3}\times 1^{5}\left(a^{2}\right)^{3}\left(a^{1}\right)^{5}$$

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

$$\left(-5\right)^{3}\times 1^{5}a^{2\times 3}a^{5}$$

Multiply 2 times 3.

$$\left(-5\right)^{3}\times 1^{5}a^{6}a^{5}$$

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

$$\left(-5\right)^{3}\times 1^{5}a^{6+5}$$

Add the exponents 6 and 5.

$$\left(-5\right)^{3}\times 1^{5}a^{11}$$

Raise -5 to the power 3.

$$-125\times 1^{5}a^{11}$$

Expand

$$-125a^{11}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-5a^{2}\right)^{3}\left(a^{1}\right)^{5}$$

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

$$\left(-5\right)^{3}\left(a^{2}\right)^{3}\times 1^{5}\left(a^{1}\right)^{5}$$

Use the Commutative Property of Multiplication.

$$\left(-5\right)^{3}\times 1^{5}\left(a^{2}\right)^{3}\left(a^{1}\right)^{5}$$

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

$$\left(-5\right)^{3}\times 1^{5}a^{2\times 3}a^{5}$$

Multiply 2 times 3.

$$\left(-5\right)^{3}\times 1^{5}a^{6}a^{5}$$

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

$$\left(-5\right)^{3}\times 1^{5}a^{6+5}$$

Add the exponents 6 and 5.

$$\left(-5\right)^{3}\times 1^{5}a^{11}$$

Raise -5 to the power 3.

$$-125\times 1^{5}a^{11}$$