Q143 of 196 Page 249

Use the properties of exponents to verify that each statement is true.
A.

B.

C. 25(5^n–2) = 5ⁿ

⇒ 4 can be written as 2².

⇒

We know that by properties of exponents,

⇒

∴

B. 4^n-1

We know that by properties of exponents,

⇒ 4^n-1 =

∴ 4^n-1 =

C. 25 (5^n-2)

⇒ 25 can also be written as 5².

⇒ 25 (5^n-2) = 5² (5^n-2)

We know that by properties of exponents, a^m × aⁿ = a^{m + n}.

⇒ 5² (5^n-2) = 5^{2 + (n-2)}

= 5^{2 + n-2}

= 5ⁿ

∴ 25 (5^n-2) = 5ⁿ

141

One Fermi is equal to 10^–15 metre. The radius of a proton is 1.3 Fermis. Write the radius of a proton in metres in standard form.

142

The paper clip below has the indicated length. What is the length in standard form.

144

Fill in the blanks

145

There are 864,00 seconds in a day. How many days long is a second?

Express your answer in scientific notation.

Use the properties of exponents to verify that each statement is true.A. B. C. 25(5n–2) = 5n