Solve 16divx^3/2(4x^-1)^2=

$$16 \div \frac { x ^ { 3 } } { 2 } ( 4 x ^ { - 1 } ) ^ { 2 } =$$

Evaluate

$$\frac{512}{x^{5}}$$

Solution Steps

Divide 16 by \frac{x^{3}}{2} by multiplying 16 by the reciprocal of \frac{x^{3}}{2}.

$$\frac{16\times 2}{x^{3}}\times \left(4x^{-1}\right)^{2}$$

Multiply 16 and 2 to get 32.

$$\frac{32}{x^{3}}\times \left(4x^{-1}\right)^{2}$$

Expand \left(4x^{-1}\right)^{2}.

$$\frac{32}{x^{3}}\times 4^{2}\left(x^{-1}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$\frac{32}{x^{3}}\times 4^{2}x^{-2}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{32}{x^{3}}\times 16x^{-2}$$

Express \frac{32}{x^{3}}\times 16 as a single fraction.

$$\frac{32\times 16}{x^{3}}x^{-2}$$

Express \frac{32\times 16}{x^{3}}x^{-2} as a single fraction.

$$\frac{32\times 16x^{-2}}{x^{3}}$$

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

$$\frac{16\times 32}{x^{5}}$$

Multiply 16 and 32 to get 512.

$$\frac{512}{x^{5}}$$

Expand

$$\frac{512}{x^{5}}$$

Solution Steps

Divide 16 by \frac{x^{3}}{2} by multiplying 16 by the reciprocal of \frac{x^{3}}{2}.

$$\frac{16\times 2}{x^{3}}\times \left(4x^{-1}\right)^{2}$$

Multiply 16 and 2 to get 32.

$$\frac{32}{x^{3}}\times \left(4x^{-1}\right)^{2}$$

Expand \left(4x^{-1}\right)^{2}.

$$\frac{32}{x^{3}}\times 4^{2}\left(x^{-1}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$\frac{32}{x^{3}}\times 4^{2}x^{-2}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{32}{x^{3}}\times 16x^{-2}$$

Express \frac{32}{x^{3}}\times 16 as a single fraction.

$$\frac{32\times 16}{x^{3}}x^{-2}$$

Express \frac{32\times 16}{x^{3}}x^{-2} as a single fraction.

$$\frac{32\times 16x^{-2}}{x^{3}}$$

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

$$\frac{16\times 32}{x^{5}}$$

Multiply 16 and 32 to get 512.

$$\frac{512}{x^{5}}$$