Question

Divide x to the 3 fifths power divided by x to the 1 fourth power.

Answer 1

Answer:

$x^{\frac{7}{20}}$

Step-by-step explanation:

$\frac{x^\frac{3}{5} }{x^\frac{1}{4} }$

To divide it we apply exponential property

$\frac{a^m}{a^n} =a^{m-n}$

when the base are same and the exponents are in division then we subtract the exponents

$\frac{x^\frac{3}{5} }{x^\frac{1}{4} }$

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

To subtract the fractions , the denominators should be same

LCD is 20

$x^{\frac{3 \cdot 4}{5 \cdot 4}-\frac{1 \cdot 5}{4 \cdot 5}}$

$x^{\frac{12}{20}-\frac{5}{20}}$

$x^{\frac{7}{20}}$

Answer 2

We can write the equation as $\frac{x^ \frac{3}{5} }{x \frac{1}{4} }$
this satisfies the law of exponent, in which a^m / a^n is equal to a^(m-n). Therefore, we can write the equation as x^(3/5  - 1/4). Simplifying further, we will have $x^{ \frac{7}{20} }$