Use the Product Rule of Exponents to simplify the expression 3^8 ⋅3^3.
To simplify the expression, we can use the Product Rule of Exponents, which states that for any nonzero numbers a and b, and any integers m and n, (a^m)⋅(a^n) = a^(m+n).
In this case, we have 3^8 ⋅ 3^3. Since the base 3 is the same in both terms, we can apply the Product Rule of Exponents to combine the exponents:
3^8 ⋅ 3^3 = 3^(8+3) = 3^11
Therefore, the expression 3^8 ⋅ 3^3 simplifies to 3^11.
Use the Product Rule of Exponents to simplify the expression 7^5 ⋅7^2.
To simplify the expression 7^5 ⋅ 7^2 using the Product Rule of Exponents, we add the exponents:
7^5 ⋅ 7^2 = 7^(5+2) = 7^7
Therefore, the expression 7^5 ⋅ 7^2 simplifies to 7^7.
Find the numerical equivalent of 7^2⋅7^3
To find the numerical equivalent of 7^2⋅7^3, we can simplify the expression using the Product Rule of Exponents:
7^2⋅7^3 = 7^(2+3) = 7^5
Calculating this value, we find:
7^5 = 7⋅7⋅7⋅7⋅7 = 16807
Therefore, the numerical equivalent of 7^2⋅7^3 is 16807.
Find the numerical equivalent of 3^9⋅3^−5
To find the numerical equivalent of 3^9⋅3^−5, we can simplify the expression using the Product Rule of Exponents:
3^9⋅3^−5 = 3^(9+(-5)) = 3^4
Calculating this value, we find:
3^4 = 3⋅3⋅3⋅3 = 81
Therefore, the numerical equivalent of 3^9⋅3^−5 is 81.
Simplify this expression using the Quotient Rule of Integer Exponents: t400t100.(1 point)
Responses
t300
t superscript 300 baseline
t4
t superscript 4 baseline
300
300
t500
t superscript 500 baseline
To simplify the expression using the Quotient Rule of Integer Exponents, we need to subtract the exponents of the same base.
t^400 ÷ t^100 = t^(400-100) = t^300
Therefore, the simplified expression is t^300.
Simplify a67b34.(1 point)
Responses
ab33
a b superscript 33 baseline
a33
a superscript 33 baseline
23
23
a67b34