Answers with Explanation.
i. If we raise a number to an exponent of 1, we get the same number.
[tex] {10}^{1} = 10[/tex]
ii. If we raise 10 to an exponent of 2, it means we multiply 10 by itself two times.
[tex] {10}^{2} = 10 \times 10 = 100[/tex]
iii. If we raise 10 to an exponent of 3, it means we multiply 10 by itself three times.
[tex] {10}^{3} = 10 \times {10}^{2} = 10 \times 100 = 1000[/tex]
iv. If we raise 10 to an exponent of 4, it means we multiply 10 by itself four times.
[tex] {10}^{4} = 10 \times {10}^{3} = 10 \times 1000 = 10000[/tex]
v. If we raise 10 to an exponent of 5, it means we multiply 10 by itself five times.
[tex] {10}^{5} = 10 \times {10}^{4} = 10 \times 10000 = 100000[/tex]
[tex] {10}^{5} = 100000[/tex]
vi. Recall that,
[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]
We apply this law of exponents to obtain,
[tex] {10}^{ - 2} = \frac{1}{{10}^{2} } = \frac{1}{100} [/tex]
vii. We apply
[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]
again to obtain,
[tex] {10}^{ - 3} = \frac{1}{ {10}^{3} } = \frac{1}{1000} [/tex]
