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.
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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
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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
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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
Links and References
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