Solve (2x^4)^5/(2x^-1)^3

$$\frac { ( 2 x ^ { 4 } ) ^ { 5 } } { ( 2 x ^ { - 1 } ) ^ { 3 } }$$

Evaluate

$$4x^{23}$$

Solution Steps

Expand \left(2x^{4}\right)^{5}.

$$\frac{2^{5}\left(x^{4}\right)^{5}}{\left(2x^{-1}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$\frac{2^{5}x^{20}}{\left(2x^{-1}\right)^{3}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{32x^{20}}{\left(2x^{-1}\right)^{3}}$$

Expand \left(2x^{-1}\right)^{3}.

$$\frac{32x^{20}}{2^{3}\left(x^{-1}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

$$\frac{32x^{20}}{2^{3}x^{-3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{32x^{20}}{8x^{-3}}$$

Cancel out 8 in both numerator and denominator.

$$\frac{4x^{20}}{x^{-3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$4x^{23}$$

Expand

$$4x^{23}$$

Solution Steps

Expand \left(2x^{4}\right)^{5}.

$$\frac{2^{5}\left(x^{4}\right)^{5}}{\left(2x^{-1}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$\frac{2^{5}x^{20}}{\left(2x^{-1}\right)^{3}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{32x^{20}}{\left(2x^{-1}\right)^{3}}$$

Expand \left(2x^{-1}\right)^{3}.

$$\frac{32x^{20}}{2^{3}\left(x^{-1}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

$$\frac{32x^{20}}{2^{3}x^{-3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{32x^{20}}{8x^{-3}}$$

Cancel out 8 in both numerator and denominator.

$$\frac{4x^{20}}{x^{-3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$4x^{23}$$