# Solved Examples on Exponents

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In this section we solved examples on exponents. These examples are solved on the basis of laws of exponents.

Examples :

1) Simplify : (2/3)-3 ÷ (4/3)-2

Solution :
(2/3)-3 ÷ (4/3)-2

As the exponents are negative first make it positive

= (3/2)3 ÷ (3/4)2

Separate the exponents

= 33/23 ÷ 32/42

= (33/23) x ( 42/32)

= [ 33-2 x (22)2]/23 [ am ÷ an = a(m-n)]

= (3 x 24)/23 [ (am)n = a(m x n)= amn]

= 3 x 24-3

= 3 x 2

= 6

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2) 43 ÷ 4-6 = 4(2n-1). Find the value of 'n'.

Solution :
43 ÷ 4-6 = 4(2n-1)

As the bases are same and there is a division so subtract the 2nd exponent from the 1st.

4[3-(-6)] = 4(2n-1)

4(3 + 6) = 4(2n-1)

49 = 4(2n-1)

As the bases are same, exponents are equal.

9 = 2n - 1

9 + 1 = 2n

10 = 2n

So, n = 10/2

n = 5

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3) n(-5)4 ÷ n2 = 5. Find the value of n.

Solution :
n(-5)4 ÷ n2 = 5

n1(-5)4/n2 = 5

n(1-2)(-5)4 = 5 [ use the division rule for 'n']

n-1(-5)4 = 5

As the exponent of 'n' is negative, make it positive.

(-5)4/n1 = 5

(-5)4/n = 5

(-5)4/5 = n [Cross multiply]

[(-5)x (-5) x (-5) x (-5)]/5 = n

625/5 = n

n = 125

Exponents

Laws of Exponents
Rational Exponents
Integral Exponents
Scientific notation
Solved examples on Scientific Notation
Solved Examples on Exponents