Question

simplify 3 to the power 1 by 5 upon 3 to the power 1 by 3 using laws of exponents​

Answer 1

Step-by-step explanation:

law used is a to the power m upon a to the power n gives a to the power (m-n)

Answer 2

Given,

3 to the power 1 by 5 upon 3 to the power 1 by 3

To Find,

Simplify using laws of exponents

Solution,

We can solve the question as follows:

It is asked that we have to simplify 3 to the power 1 by 5 upon 3 to the power 1 by 3 using laws of exponents​.

The given expression is:
$= \frac{3^{\frac{1}{5} } }{3^{\frac{1}{3} } }$

According to the laws of exponents, when two exponents with the same base are divided, we subtract the exponent in the denominator with the exponent in the numerator.

For example, let the base be a and the exponents be x and y.

$\frac{a^{x} }{a^{y} } = a^{x - y}$

Therefore,

$= \frac{3^{\frac{1}{5} } }{3^{\frac{1}{3} } }$

$=3^{\frac{1}{5} - \frac{1}{3} }$

$= 3^{\frac{3- 5}{15} }$

$= 3^{\frac{-2}{15} }$

Hence, the result if 3^-2/15.