PRODUCT RULE AND QUOTIENT RULE

Question 1.

Calculate (B¹⁰ x B⁵) / B¹² =

Product Rule – When exponential expressions multiply and the bases are the same, you can just add the exponents. 

Example, let’s look at m exponent 3, times m exponent 4.

Because they both have the same bases, which is m in this case, we can just add the exponents.

So this will be m exponent 3 + 4, which is m exponent 7.

 

Quotient Rule – When terms with exponents  divide and the bases are the same, then you can simply subtract the exponents. 

So m exponent 5 divided by m exponent 2, will be m exponent 5 minus 2, which is m exponent 3.

So for our question, we can see that they all have the base of B, so the rules can apply.

So B exponent 10 is multiplying B exponent 5, so we can add the exponents to get B exponent 10 + 5. This will give us B exponent 15.

This B exponent 15 is being divided by B exponent 12.

We know that when terms with the same base divide, we can simply subtract their exponent.

So we have B exponent 15 minus 12, which is B exponent 3.

So this is the answer.

Nothing New here. Everything is just a repetition.

 

EXPONENT 1 AND EXPONENT 0

Question 2.

Simplify x⁹ ÷ x⁹ +  x⁰.

Here, we are applying the rules of exponents to solve it.

We know from the quotient rule of exponent that when terms divide and the bases are the same you can juts subtract the exponents. 

We have x exponent 9 divided by x exponent 9. since the base of both are x, we subtract the exponents, 9 minus 9. this will give us x exponent 0.

We know that any number exponent zero is 1.

so this is 1.

We have x exponent zero here also. This is 1

Now we have 1 + 1, which gives us 2 as the answer .