Question

Write the simplified ( form) value of (49)_1/4 ÷ (49)1/4

Answer 1

please ask in maths section

Answer 2

The value of $(49)^{-\dfrac{1}{4}}$ ÷ $(49)^{\dfrac{1}{4}}$ = $\dfrac{1}{7}$

Explanation:

We have,

$(49)^{-\dfrac{1}{4}}$ ÷ $(49)^{\dfrac{1}{4}}$

To find, the value of $(49)^{-\dfrac{1}{4}}$ ÷ $(49)^{\dfrac{1}{4}}$ = ?

∴ $(49)^{-\dfrac{1}{4}}$ ÷ $(49)^{\dfrac{1}{4}}$

$=\dfrac{(49)^{-\dfrac{1}{4}}}{(49)^{\dfrac{1}{4}}}$

$=49^{-\dfrac{1}{4}}.49^{-\dfrac{1}{4}}$

$=49^{-\dfrac{1}{4}-\dfrac{1}{4}}$

Using the identity,

$a^{m}.a^{n} =a^{m+n}$

$=49^{\dfrac{-1-1}{4}}$

$=49^{\dfrac{-1}{2}}$

$=(7^{2}) ^{\dfrac{-1}{2}}$

= $7^{-1}$

= $\dfrac{1}{7}$

Thus, the value of $(49)^{-\dfrac{1}{4}}$ ÷ $(49)^{\dfrac{1}{4}}$ = $\dfrac{1}{7}$