Question

If a^7 = 7,777 and a^6/b = 11, what is the value of ab?

Answer 1

Answer:

The value of ab=707.

Step-by-step explanation:

Given: a^7 = 7,777  &  a^6/b = 11.

To find the value of ab.

Multiply numerator & denominator in a^6/b = 11 by a we have.

$\frac{a^{6} }{b}=\frac{a^{7} }{ab}$

$\frac{a^{7} }{ab}=11$

Substitute a^7 = 7,777 we have:

$\frac{7777 }{ab}=11\\ab=707$

Therefore the value of ab=707.

#SPJ2

Answer 2

Given:

a⁷ = 7777             ----------------- (i)

a⁶/b = 11               ---------------- (ii)

Find:

The value of ab.

Answer:

The value of ab is 707.

Solution:

Method I:

Given that a⁷ = 7777   (From (i))

We can write a⁷ as a⁶⁺¹.

∴ a⁶⁺¹ = 7777

a⁶.a = 7777

a⁶ = 7777/a

Now, from (ii), we hve

a⁶/b = 11    --------------- (iii)

But from (iii), we have a⁶ = 7777/a

∴ 7777/ab = 11

ab = 7777/11

ab = 707

Method II:

Taking (ii), we have

a⁶/b = 11

Multiplying and dividing by 'a' on L.H.S., we get

(a⁶×a)/(b×a) = 11

a⁶⁺¹/ab = 11

a⁷/ab = 11

But from (ii), we have a⁷ = 7777

∴ 7777/ab = 11

ab = 7777/11

ab = 707

Hence, the value of ab is 707.

#SPJ2