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.