Question

The value of (5⁷÷5⁶)² is ______​

Answer 1

We have:

$(\dfrac{5^7}{5^6})^{2}$

We have to fond, the value of $(\dfrac{5^7}{5^6})^{2}$.

Solution:

∴ $(\dfrac{5^7}{5^6})^{2}$

= $\dfrac{(5^7)^2}{(5^6)^2}$ [ ∵ $(\dfrac{a}{b})^m= \dfrac{a^m}{b^m}$]

= $\dfrac{5^{14}}{5^{12}}$  [ ∵ $(a^m)^{n} =a^{mn}$]

= $5^{14-12}$  [ ∵ $\dfrac{a^m}{a^n}=a^{m-n}$]

= $5^2$

= 25

∴ $(\dfrac{5^7}{5^6})^{2}$ = 25

Thus, the value of $(\dfrac{5^7}{5^6})^{2}$ is equal to "25".

Answer 2

Given:

(5⁷÷5⁶)²

To find:

The value of the given expression

Solution:

We have given the term as:

(5⁷÷5⁶)²

as per the rule of the exponents when the base is same then in the division the power get subtracted so we get the term as:

(5⁷⁻⁶)²

(5¹)²

As per the rule of the exponent, the power over the power gets multiplied so we get the term as:

5²

5×5

25

The value of the given expression (5⁷÷5⁶)² is 25