Write each expression using a single exponent.

34.) 5^10/5^7

36.) 76^11/76^5

Please, Please, show work.

when dividing, just subtract exponents:

5^10 / 5^7 = 5^(10-7) = 5^3
because
5^10 = 5*5*5*5*5*5*5*5*5*5
5^7 = 5*5*5*5*5*5*5
divide, and seven of the 5's cancel, leaving only 3 in top: 5^3

76^11 / 76^5 = 76^(11-5) = 76^6

wrong

34.) To simplify the expression 5^10/5^7, we can subtract the exponents because the bases are the same.

Starting with 5^10/5^7, we have:

5^(10-7)

Simplifying the exponent, we get:

5^3

So, 5^10/5^7 can be written as 5^3.

36.) To simplify the expression 76^11/76^5, we can again subtract the exponents because the bases are the same.

Starting with 76^11/76^5, we have:

76^(11-5)

Simplifying the exponent, we get:

76^6

So, 76^11/76^5 can be written as 76^6.

To write each expression using a single exponent, we can use the rule of exponents which states that for any non-zero number "a" and integers "m" and "n":

a^m / a^n = a^(m - n)

Let's apply this rule to each expression:

34.) 5^10 / 5^7

Using the exponent rule, we subtract the exponents:

5^(10 - 7)

Simplifying the exponent, we get:

5^3

Therefore, the expression 5^10 / 5^7 can be written as 5^3.

36.) 76^11 / 76^5

Using the exponent rule, we subtract the exponents:

76^(11 - 5)

Simplifying the exponent, we get:

76^6

Therefore, the expression 76^11 / 76^5 can be written as 76^6.