Question

please tell full solution
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Answer 1

Answer:

[9(³√64 + ³√125)³]^(0.25) = 9

Step-by-step explanation:

We have,

[9(³√64 + ³√125)³]^(0.25)

Now,

We need to know certain values and solving helpers to solve this problem,

We must know that,

³√64 = ³√(2³ × 2³)

= 2 × 2

= 4

So,

³√64 = 4 ------ 1

Similarly,

³√125 = ³√(5³)

= 5

So,

³√125 = 5 ------ 2

Also we should know that,

0.25 = (1/4) ------- 3

And we must know that,

(a^m) × (b^m) = (a × b)^m ------ 4

Also,

(a^m)^n = a^(m × n) ------ 5

Then we can solve the problem,

[9(³√64 + ³√125)³]^(0.25)

From eq.1, eq.2 and eq.3 we get,

= [9(4 + 5)³]^(1/4)

= [9¹ × (9)³]^(1/4)

Using the eq.4

= [9^(1 + 3)]^(1/4)

= [9⁴]^(1/4)

Using eq.5 we get,

= 9^(4 × (1/4))

= 9^(4/4)

= 9¹

= 9

Hence,

[9(³√64 + ³√125)³]^(0.25) = 9

Hope it helped you and believing you understood it...All the best