Question

Express 3^5 : 3^8 in simplest form

Answer 1

Given:

 $3^{5}$:$3^{8}$

To Find:

Simplest form

Solution:

When exponents are in a  ratio having a common base, then we subtract the exponents.

Now,

⇒ $3^{5}$:$3^{8}$

⇒ $\frac{3^{5} }{3^{8} }$ = $3^{(5-8)}$

⇒$\frac{3^{5} }{3^{8} }$ = $3^{(-3)}$

⇒$\frac{3^{5} }{3^{8} }$ =$\frac{1}{3^{3} }$

⇒$\frac{3^{5} }{3^{8} }$ =$\frac{1}{27}$

Hence, the simplest form of  $3^{5}$:$3^{8}$ is $\frac{1}{27}$.

Answer 2

Answer: 1/27 is the simplest form.

Step-by-step explanation:

Indices Multiplication rules are as follows:

1. Multiplication rule with same base -

$p^n * p^m = p^ (n+m)$

2. Multiplication rule with same indices

$p^n * y^n = (p* y)^n$

Indices division rules are as follows:

1. Division rule with same base -

$p^m / p^n = p^(m - n)$

2. Division rule with same indices -

$x^n / y^n = (x / y)^n$

Step 1: $3^5 : 3^8 = 3^5/3^8$

Step 2: $3^5/3^8 = 3^5/3^(5+3)$

Step 3: $3^5/3^(5+3) = 3^5/(3^5*3^3)$ (from multiplication rule with same base)

Step 4:$3^5/(3^5*3^3) =1/3^3$ (cancelling the term $3^5$ from both the numerator                 and denominator)

Final ans: $1/3^3 = 1/27$