Question

simplify (81)^1/3÷(81)^1/12​

Answer 1

Answer:

3

Step-by-step explanation:

(81)^1/3÷(81)^1/12= 81^1/3-1/12

81^1/4= 3

Answer 2

Answer:

The value of the expression $(81)^{1/3}\div (81)^{1/12}$ is $3$.

Step-by-step explanation:

Recall the laws of exponent,

(i) $(a^m)^n=a^{mn}$

(ii) $a^ma^n=a^{m+n}$

(iii) $\frac{a^m}{a^n}=a^{m-n}$

Step 1 of 2

Consider the given expression as follows:

$(81)^{1/3}\div (81)^{1/12}$

Using the property (iii) law of exponent, we get

$(81)^{\frac{1}{3}-\frac{1}{12} }$

Simplify as follows:

⇒ $(81)^{\frac{4-1}{12} }$

⇒ $(81)^{3/12}$

⇒ $(81)^{1/4}$ . . . . . (1)

Step 2 of 2

Prime factorisation of the number $81$ is,

$81=3\times 3\times 3\times 3$

Rewrite the number $81$ as follows:

$81=3^4$

Substitute the value $3^4$ for $81$ in the expression (1) as follows:

⇒ $(81)^{1/4}=(3^4)^{1/4}$

Using the property (i) of law of exponents, we get

⇒ $(81)^{1/4}=(3)^4^{(\frac{1}{4} )}$

Simplify as follows:

⇒ $(81)^{1/4}=3^{4/4}$

⇒ $(81)^{1/4}=3^1$

               $=3$

Final answer: Therefore, the value of the expression $(81)^{1/3}\div (81)^{1/12}$ is $3$.

#SPJ2