# Solved Examples on Exponents

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**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}[ a

^{m}÷ a

^{n}= a

^{(m-n)}]

= (3 x 2

^{4})/2

^{3}[ (a

^{m})

^{n}= a

^{(m x n)}= a

^{mn}]

= 3 x 2

^{4-3}

= 3 x 2

= 6

_________________________________________________________________

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

__________________________________________________________________

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

• Laws of Exponents

• Rational Exponents

• Integral Exponents

• Scientific notation

• Solved examples on Scientific Notation

• Solved Examples on Exponents

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