Question

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Answer 1

We are given the following two expressions

`5^8\cdot5^2\quad and\quad (5^(20))/(5^2)`

Let us simply both expressions.

For the 1st expression, recall the product rule of exponents given by

`a^x\cdot a^y=a^(x+y)`

Applying the above rule to the 1st expression

`5^8\cdot5^2=5^(8+2)=5^(10)`

For the 2nd expression, recall the quotient rule of exponents given by

`(a^x)/(a^y)=a^(x-y)`

Applying the above rule to the 2nd expression

`(5^(20))/(5^2)=5^(20-2)=5^(18)`

As you can see, both expressions are not equivalent.

Therefore, the correct answer is option C

`5^8\cdot5^2=5^(10)\quad and\quad (5^(20))/(5^2)=5^(18)`