Question

i) simplify (2/5)⁴×(2/5)⁵÷(2/5)⁹
ii) simplify [{(3/2)⁷÷(3/2)⁹}×(3/2)²
(both answers are 1)
please help me
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Answer 1

Answer:

Hello!

Hai friend,

here is your answer

(2/5)³ ×(2/5)² × (2/5)^-4

Formula a^m *a^n = a^m+n

=(2/5)^ 3+2-4

=(2/5)^5-4

=(2/5)^1

=2/5

=0.4

∴The answer is 2/5 or 0.4

(2/5)³ ×(2/5)² × (2/5)-⁴ =2/5=0.4

hope helped!!

Step-by-step explanation:

Answer 2

Law 1

$\large { {a}^{m} \times {a}^{n} = {a}^{m + n} }$

i.e., when the bases are equal, the powers are also equal, hence you can add them in case of multiplication.

Law 2

$\large { \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }$

i.e., when ths bases are equal, the powers are also equal, hence you can subtract the power of the denominator from the numerator's power.

Law 3

$\large {{a}^{0} = 1}$

i.e., any number raised to the power 0 is always 1, what ever it may be.

In case of multiple operations like multiplication and division at the same time, use BODMAS to calculate the powers and omit the bases if they are equal but don't forget to place them again at the end of your answer, to get the required answer.

I hope this helped you.