In a repeater machine with 0 as an exponent, the base machine is applied 0 times.
(a) What do these machines do to a piece of chalk?
(b) What do you think the value of 6⁰ is?
You have seen that a hookup of repeater machines with the same base can be replaced by a single repeater machine. Similarly, when you multiply exponential expressions with the same base, you can replace them with a single expression.
Solution:
Given a repeater machine with 0 as an exponent, the base machine is applied 0 times.
(a) We have to find the work done by the machine to a piece of chalk.
A repeater machine is a hypothetical machine which automatically enlarges items several times.
Using the law of exponents,
a⁰ = 1, where a ≠ 0
From the given machines,
×3⁰ = 1
×13⁰ = 1
×29⁰ = 1
Therefore, these machines do nothing to a piece of chalk.
(b) We have to find the value of 6⁰.
Using the law of exponents,
a⁰ = 1, where a ≠ 0
So, 6⁰ = 1
Therefore, the required value is 1.
✦ Try This: In a repeater machine with 0 as an exponent, the base machine is applied 0 times. What do these machines do to a piece of chalk?
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12
NCERT Exemplar Class 8 Maths Chapter 8 Problem 153
In a repeater machine with 0 as an exponent, the base machine is applied 0 times. (a) What do these machines do to a piece of chalk, (b) What do you think the value of 6⁰ is? You have seen that a hookup of repeater machines with the same base can be replaced by a single repeater machine. Similarly, when you multiply exponential expressions with the same base, you can replace them with a single expression
Summary:
In a repeater machine with 0 as an exponent, the base machine is applied 0 times. (a) These machines do nothing to a piece of chalk, (b) The value of 6⁰ is 1.
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