Question

(3⁴)²÷[3⁴*3⁵],Evaluate it.

Answer 1

( 3⁴ )² ÷ [3⁴ × 3⁵ ]

$\implies3^{4\times2}\div\{3^4\times3^5\}$

$=3^8\div\{3^{4+5}\}$

$=3^8\div3^9$

$=\frac{3^8}{3^9}$

$=3^{8-9}$

$=3^{-1}$

$=\frac{1}{3}$

hence, answer is 1/3

Answer 2

Q. Evaluate $(3^{4}) ^{2}$ ÷ $[3^{4} \times 3^{5}]$

Solution :

[When we have power raised to another power, we have to multiply both the powers.]

⇒ $3^{4 \times 2}$ ÷ $[3^{4} \times 3^{5}]$

⇒ $3^{8} ÷ [3^{4} \times 3^{5}]$

[Since, we have same base for both numerator and denominator, we have to combine the powers.]

⇒ $3^{8}$ ÷ $[3^{4+5} ]$

⇒ $3^{8} ÷ 3^{9}$

⇒ $\frac{3^{8}}{3^{9}}$

⇒ $3^{8 - 9}$

⇒ $3^{-1}$

[Whenever we have a negative number as exponent and we need to make it as positive, we have to flip the base that is write the reciprocal of the base and change the negative exponent as positive exponent. (i.e., $\frac{1}{a^{n}})$]

⇒ Reciprocal of the integer 3 is $\frac{1}{3}$

Hence, the answer is $\frac{1}{3}$