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 3^8 ⋅3^3.
23 answers
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.
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.
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.
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
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.
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
Responses
ab33
a b superscript 33 baseline
a33
a superscript 33 baseline
23
23
a67b34
To simplify the expression a^67b^34, we cannot combine the terms because the bases are different. Therefore, the expression remains as it is: a^67b^34.
Apply the Quotient Rule of Integer Exponents to simplify 2365÷2332.(1 point)
Responses
2333
23 superscript 33 baseline
97
97
2397
23 superscript 97 baseline
133
Responses
2333
23 superscript 33 baseline
97
97
2397
23 superscript 97 baseline
133
To simplify the expression 2365 ÷ 2332 using the Quotient Rule of Integer Exponents, we need to subtract the exponents involved:
2365 ÷ 2332 = 23^(65-32) = 23^33
Therefore, the simplified expression is 23^33.
2365 ÷ 2332 = 23^(65-32) = 23^33
Therefore, the simplified expression is 23^33.
Simplify this expression using the Quotient Rule of Integer Exponents: 1253÷753.(1 point)
Responses
1253÷753
12 superscript 53 baseline divided by 7 superscript 53 baseline
12106
12 superscript 106 baseline
5106
5 superscript 106 baseline
553
Responses
1253÷753
12 superscript 53 baseline divided by 7 superscript 53 baseline
12106
12 superscript 106 baseline
5106
5 superscript 106 baseline
553
To simplify the expression 1253 ÷ 753 using the Quotient Rule of Integer Exponents, we need to subtract the exponents involved:
1253 ÷ 753 = 12^(53-53) = 12^0
Any non-zero number raised to the power of 0 is equal to 1. Therefore, the simplified expression is 1.
1253 ÷ 753 = 12^(53-53) = 12^0
Any non-zero number raised to the power of 0 is equal to 1. Therefore, the simplified expression is 1.
wrong
Apologies for the mistake.
To simplify 1253 ÷ 753 using the Quotient Rule of Integer Exponents, we need to subtract the exponents involved:
1253 ÷ 753 = 1^(1253-753) = 1^500
Any non-zero number raised to the power of 0 is equal to 1. Therefore, the simplified expression is 1.
To simplify 1253 ÷ 753 using the Quotient Rule of Integer Exponents, we need to subtract the exponents involved:
1253 ÷ 753 = 1^(1253-753) = 1^500
Any non-zero number raised to the power of 0 is equal to 1. Therefore, the simplified expression is 1.
which one should i pick
I apologize for the incorrect responses. The correct way to simplify the expression 1253 ÷ 753 using the Quotient Rule of Integer Exponents is to subtract the exponents:
1253 ÷ 753 = 12^(53-53) = 12^0
Any non-zero number raised to the power of 0 is equal to 1. Therefore, the simplified expression is 1.
1253 ÷ 753 = 12^(53-53) = 12^0
Any non-zero number raised to the power of 0 is equal to 1. Therefore, the simplified expression is 1.
Responses
1253÷753
12 superscript 53 baseline divided by 7 superscript 53 baseline
12106
12 superscript 106 baseline
5106
5 superscript 106 baseline
553
1253÷753
12 superscript 53 baseline divided by 7 superscript 53 baseline
12106
12 superscript 106 baseline
5106
5 superscript 106 baseline
553
Apologies for the previous incorrect responses.
To simplify the expression 1253 ÷ 753 using the Quotient Rule of Integer Exponents, we do not need to apply any exponent rules as this is a regular division of numbers. Therefore, the simplified expression is indeed:
1253 ÷ 753
To simplify the expression 1253 ÷ 753 using the Quotient Rule of Integer Exponents, we do not need to apply any exponent rules as this is a regular division of numbers. Therefore, the simplified expression is indeed:
1253 ÷ 753
Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?(1 point)
Responses
Check if the bases are the same; if they are, add the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Check if the bases are the same; if they are, add the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Responses
Check if the bases are the same; if they are, add the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Check if the bases are the same; if they are, add the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
The correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents are:
1. Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator.
2. Write the resulting expression in exponential form.
Therefore, the correct option is:
Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
1. Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator.
2. Write the resulting expression in exponential form.
Therefore, the correct option is:
Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.