How to solve questions on exponents in maths?. Detailed solutions to the questions on exponents in math are presented.
Detailed Solutions to Questions on Exponents.

Write the following using exponents:
a) 8 × 8 × 8 × 8
b) 10 × 10 × 10 × 10 × 10 × 10 × 10
c) A × A × A
d) meter × meter
e) centimeter × centimeter × centimeter
Solution
Use the definition of an exponent.
a) 8 × 8 × 8 × 8 = 8^{ 4} , 8 multiplied by itself 4 times.
b) 10 × 10 × 10 × 10 × 10 × 10 × 10 = 10^{ 7
c) A × A × A = A 3
d) meter × meter = meter 2
e) centimeter × centimeter × centimeter = centimeter 3}

Evaluate the following:
a) 2^{ 4}
b) 10^{ 4}
c) (2)^{ 4}
d) 2^{ 4}
Solution
Use the definition of an exponent.
a) 2^{ 4} = 2 × 2 × 2 × 2 = 16
b) 10^{ 4} = 10 × 10 × 10 × 10 = 10,000
c) (2)^{ 4} = (2) × (2) × (2) × (2) = 16
d) 2^{ 4} =  2 × 2 × 2 × 2 =  16

Use exponents to write the following using one power only.
a) 4 × 8
b) 25 × 5
c) 16 × 4 × 4^{ 3}
d) 2 × 2 × 8 × 2^{ 3}
e) B × B × B^{ 3}
Solution
a) Express 4 and 8 as products of 2 then use exponents.
4 × 8 = (2 × 2) × (2 × 2 × 2) = 2 × 2 × 2 × 2 × 2 = 2^{ 5}
b) Express 25 as products of 5 then use exponents.
25 × 5 = (5 × 5) × 5 = 5 × 5 × 5 = 5^{ 3}
c) Express all terms as products of 4 then use exponents.
16 × 4 × 4^{ 3} = (4 × 4) × 4 × (4 × 4 × 4) = 4 × 4 × 4 × 4 × 4 × 4 = 4^{ 6}
d) Express all terms as products of 2 then use exponents.
2 × 2 × 8 × 2^{ 3} = 2 × 2 × (2 × 2 × 2) × (2 × 2 × 2) = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2^{ 8}
e) Express all terms as products of B then use exponents.
B × B × B^{ 3} = B × B ×(B × B × B) = B × B × B × B × B = B ^{ 5}

Use exponents to rewrite the following expressions in simplified forms.
a) 2^{ 3} × 2^{ 4}
b) 6 × 6^{ 3}
c) 5 × 5^{ 2} × 5^{ 3}
Solution
a) Use the definition of exponents to write expressions as product of 2 then rewrite as in exponent form.
2^{ 3} × 2^{ 4} = (2 × 2 × 2) × (2 × 2 × 2 × 2) = 2^{ 7}
b) Use the definition of exponents to write expressions as product of 6 then rewrite as in exponent form.
6 × 6^{ 3} = 6 × (6 × 6 × 6) = 6^{ 4}
c) Use the definition of exponents to write expressions as product of 5 then rewrite as in exponent form.
5 × 5^{ 2} × 5^{ 3} = 5 × (5 × 5) ×( 5× 5 × 5) = 5^{ 6}

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