How do you find the product of (3x^3)/(8x)*16/x?

Jul 24, 2017

You will need to multiply the numbers top X top, and bottom X bottom and add the exponents in the same way. After that you will need to simplify by dividing and exponent subtraction if necessary.

Explanation:

We have: $\frac{3 {x}^{3}}{8 x} \cdot \frac{16}{x}$

$\frac{3 {x}^{3}}{8 x} \cdot \frac{16}{x} = \frac{48 {x}^{3}}{8 {x}^{2}} \to$ by multiplying $3 {x}^{3} \cdot 16 = 48 {x}^{3}$ and adding exponents to get the denominator: $8 x \cdot x = 8 {x}^{2}$

$\frac{48 {x}^{3}}{8 {x}^{2}} = \frac{\cancel{48 {x}^{3}} 6 x}{\cancel{8 {x}^{2}}} = 6 x \to$ by dividing $\frac{48}{8}$ and subtracting exponents to reduce the fraction: ${x}^{3} / {x}^{2} = x$

Then: $\frac{3 {x}^{3}}{8 x} \cdot \frac{16}{x} = 6 x$

Jul 24, 2017

$6 x$

Explanation:

$\frac{3 {x}^{3}}{8 x} \times \frac{16}{x}$

If you cancel factors in the numerator and denominator first, it makes the numbers smaller.

Cancel the numbers and simplify the variables in the denominators by adding the indices:

$\frac{3 {x}^{3}}{\cancel{8} x} \times {\cancel{16}}^{2} / x = \frac{6 {x}^{3}}{{x}^{2}}$

To divide with indices, subtract them:

$\frac{6 {x}^{3}}{{x}^{2}} = 6 x$