Question

Which of the following expressions is equivalent to the one shown below?

Answer 1

The equivalent expression is
`7^(6)` ⇒ answer A

Explanation:

* Lets revise some rules of the exponents

- In the exponential functions we have some rules

# In multiplication if we have same base then add the power

b^m × b^n = b^(m + n)

- Ex:
`5^(11)*5^(4)=5^(11+4)=5^(15)`

# In division if we have same base we subtract the power

b^m ÷ b^n = b^(m – n)

- Ex:
`(3^(10))/(3^(4))=3^(10-4)=3^(6)`

* Now lets solve the problem

- There is the expression
`(7^(13))/(7^(7))`

- We have base 7 up and down

∵ In division if we have same base we subtract the power

∵ The base up is 7 and the base down is 7

- We will subtract the powers

∴
`(7^(13))/(7^(7))=7^(13-7)=7^(6)`

∴ The answer is
`7^(6)`

* The equivalent expression is
`7^(6)`

Answer 2

A (7^6)

Explanation:

Step 1: Find the property of 7^13/7^7

b^m/b^n=b^m-n

Therefore, when the numerator and denominator are the same number, the powers can be subtracted to simplify the answer.

Step 2: Apply the property to the question

7^13/7^7 = 7^13-7

=7^6

Hence, option A is the correct answer.

!!