Question

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

Answer 1

Answer:

The equivalent expression is $7^{6}$ ⇒ answer A

Step-by-step 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: $\frac{3^{10}}{3^{4}}=3^{10-4}=3^{6}$

* Now lets solve the problem

- There is the expression $\frac{7^{13}}{7^{7}}$

- 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

∴ $\frac{7^{13}}{7^{7}}=7^{13-7}=7^{6}$

∴ The answer is $7^{6}$

* The equivalent expression is $7^{6}$

Answer 2

Answer:

A (7^6)

Step-by-step 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.

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