Solved Examples on Exponents

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

= 3
3 /2 3 ÷ 3 2 /4 2

= (3
3 /2 3 ) x ( 4 2 /3 2 )

= [ 3
3-2 x (2 2 ) 2 ]/2 3 [ am ÷ an = a(m-n)]

= (3 x 2
4 )/2 3 [ (am)n = a(m x n)= amn]

= 3 x 2
4-3

= 3 x 2

= 6

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2) 4
3 ÷ 4 -6 = 4 (2n-1) . Find the value of 'n'.

Solution :
4
3 ÷ 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)

4
9 = 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 ÷ n 2 = 5. Find the value of n.

Solution :
n(-5)
4 ÷ n 2 = 5

n
1 (-5) 4 /n 2 = 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 /n 1 = 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