Solve (5x^-4)^-4(2x^3)^-5

$$( 5 x ^ { - 4 } ) ^ { - 4 } ( 2 x ^ { 3 } ) ^ { - 5 }$$

Evaluate

$$\frac{x}{20000}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(5x^{-4}\right)^{-4}\times \left(2x^{3}\right)^{-5}$$

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

$$5^{-4}\left(x^{-4}\right)^{-4}\times 2^{-5}\left(x^{3}\right)^{-5}$$

Use the Commutative Property of Multiplication.

$$5^{-4}\times 2^{-5}\left(x^{-4}\right)^{-4}\left(x^{3}\right)^{-5}$$

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

$$5^{-4}\times 2^{-5}x^{-4\left(-4\right)}x^{3\left(-5\right)}$$

Multiply -4 times -4.

$$5^{-4}\times 2^{-5}x^{16}x^{3\left(-5\right)}$$

Multiply 3 times -5.

$$5^{-4}\times 2^{-5}x^{16}x^{-15}$$

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

$$5^{-4}\times 2^{-5}x^{16-15}$$

Add the exponents 16 and -15.

$$5^{-4}\times 2^{-5}x^{1}$$

Raise 5 to the power -4.

$$\frac{1}{625}\times 2^{-5}x^{1}$$

Raise 2 to the power -5.

$$\frac{1}{625}\times \frac{1}{32}x^{1}$$

Multiply \frac{1}{625} times \frac{1}{32} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{1}{20000}x^{1}$$

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

$$\frac{1}{20000}x$$

Expand

$$\frac{x}{20000}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(5x^{-4}\right)^{-4}\times \left(2x^{3}\right)^{-5}$$

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

$$5^{-4}\left(x^{-4}\right)^{-4}\times 2^{-5}\left(x^{3}\right)^{-5}$$

Use the Commutative Property of Multiplication.

$$5^{-4}\times 2^{-5}\left(x^{-4}\right)^{-4}\left(x^{3}\right)^{-5}$$

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

$$5^{-4}\times 2^{-5}x^{-4\left(-4\right)}x^{3\left(-5\right)}$$

Multiply -4 times -4.

$$5^{-4}\times 2^{-5}x^{16}x^{3\left(-5\right)}$$

Multiply 3 times -5.

$$5^{-4}\times 2^{-5}x^{16}x^{-15}$$

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

$$5^{-4}\times 2^{-5}x^{16-15}$$

Add the exponents 16 and -15.

$$5^{-4}\times 2^{-5}x^{1}$$

Raise 5 to the power -4.

$$\frac{1}{625}\times 2^{-5}x^{1}$$

Raise 2 to the power -5.

$$\frac{1}{625}\times \frac{1}{32}x^{1}$$

Multiply \frac{1}{625} times \frac{1}{32} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{1}{20000}x^{1}$$

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

$$\frac{1}{20000}x$$