Solve Questions on Exponents  Grade 7 Maths Questions With Detailed Solutions
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
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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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