Use the Product Rule of Exponents to simplify the expression 3^8 ⋅3^3.

23 answers

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
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
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.
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
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.
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.
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.
Responses

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
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.
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.