Solve (2x^2)^3*(5x^-2)^3=

$$( 2 x ^ { 2 } ) ^ { 3 } \times ( 5 x ^ { - 2 } ) ^ { 3 } =$$

Evaluate

$$1000$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

$$2^{3}\times 5^{3}x^{2\times 3}x^{-2\times 3}$$

Multiply 2 times 3.

$$2^{3}\times 5^{3}x^{6}x^{-2\times 3}$$

Multiply -2 times 3.

$$2^{3}\times 5^{3}x^{6}x^{-6}$$

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

$$2^{3}\times 5^{3}x^{6-6}$$

Add the exponents 6 and -6.

$$2^{3}\times 5^{3}x^{0}$$

Raise 2 to the power 3.

$$8\times 5^{3}x^{0}$$

Raise 5 to the power 3.

$$8\times 125x^{0}$$

Multiply 8 times 125.

$$1000x^{0}$$

For any term t except 0, t^{0}=1.

$$1000\times 1$$

For any term t, t\times 1=t and 1t=t.

$$1000$$

Factor

$$2^{3}\times 5^{3}$$