Asked by GhostGirl

Use the Product Rule of Exponents to simplify the expression 24 ⋅22
Answered by GhostGirl
wrong
Answered by GhostGirl
ok bot its 2 to the 4th power times 2 to the 2nd power what's the answer.
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Use the Product Rule of Exponents to simplify the expression 38 ⋅33.
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Use the Product Rule of Exponents to simplify the expression 75 ⋅72
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bot what is 7^5 times 7^2
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7^2 times 7^3
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Find the numerical equivalent of 7^2⋅7^3
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Find the numerical equivalent of 3^9⋅3−5
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Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
Responses

(52)9
left parenthesis 5 squared right parenthesis superscript 9 baseline

327
32 superscript 7 baseline

62⋅73
6 squared times 7 cubed

108⋅108
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are you sure?
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bot you have to choose and answers so which one is it?
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ok are you sure its correct?
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Which of the following correctly used the Product Rule of Exponents to simplify the expression 100^8⋅100^7?(1 point)
Responses

10056
100 superscript 56 baseline

10015
100 superscript 15 baseline

20015
200 superscript 15 baseline

10,00015
Answered by GhostGirl
Find the numerical equivalent of 102 ⋅103(1 point)
Responses

1,100
1,100

105
10 superscript 5 baseline

10
10

100,000
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Find the numerical equivalent of 25 ⋅2−2(1 point)
Responses

8
8

2
2

128
128

16
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that's not an answers
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Find the numerical equivalent of 2^5 ⋅2−2
Answered by GhostGirl
4^9 times 4-7
Answered by GPT 3.5
The product rule of exponents states that when multiplying two numbers with the same base, you add the exponents.

So, applying the product rule of exponents to 24 ⋅ 22, we get:

24 ⋅ 22 = 2(4+2) = 2^6 = 64
Answered by GPT 3.5
I apologize for the mistake. Let's correct it.

Using the product rule of exponents, we have:

24 ⋅ 22 = (2^4) ⋅ (2^2)

According to the product rule of exponents, we can add the exponents of the same base when multiplying.

So, 24 ⋅ 22 = 2^(4+2) = 2^6

Therefore, 24 ⋅ 22 simplifies to 2^6, which is equal to 64.
Answered by GPT 3.5
My apologies for the confusion. Let's simplify the expression correctly.

When multiplying two numbers with the same base, we add the exponents. So:

24 ⋅ 22 = (2^4) ⋅ (2^2) = 2^(4+2) = 2^6

Therefore, 24 ⋅ 22 simplifies to 2^6, which is equal to 64.
Answered by GPT 3.5
The product rule of exponents states that when multiplying two numbers with the same base, you add the exponents.

So, applying the product rule of exponents to 38 ⋅ 33, we get:

38 ⋅ 33 = 3(8+3) = 3^11
Answered by GPT 3.5
To use the product rule of exponents, we first express each number in terms of the same base. In this case, both numbers are expressed in terms of 2.

75 ⋅ 72 = (5⋅15) ⋅ (3⋅24)

Next, we apply the product rule of exponents, which states that when multiplying two numbers with the same base, we add the exponents.

= 5⋅3 ⋅ 15⋅24

Now, we simplify the multiplication:

= 15 ⋅ 360

= 5400

Therefore, 75 ⋅ 72 simplifies to 5400.
Answered by GPT 3.5
To simplify the expression 7^5 times 7^2, we can use the product rule of exponents. According to this rule, when multiplying two numbers with the same base, we add the exponents.

Therefore, 7^5 times 7^2 can be written as 7^(5+2).

Adding the exponents, we have 7^7.

Therefore, 7^5 times 7^2 simplifies to 7^7.
Answered by GPT 3.5
To simplify the expression 7^2 times 7^3, we can apply the product rule of exponents. This rule states that when multiplying two numbers with the same base, we add their exponents.

So, 7^2 times 7^3 can be written as 7^(2+3).

Adding the exponents, we get 7^5.

Therefore, 7^2 times 7^3 simplifies to 7^5.
Answered by GPT 3.5
To find the numerical equivalent of 7^2⋅7^3, we can simplify the expression by applying the product rule of exponents. This rule states that when multiplying two numbers with the same base, we add their exponents.

Therefore, 7^2⋅7^3 can be written as 7^(2+3) = 7^5.

To find the numerical value of 7^5, we can simply calculate it:

7^5 = 7 × 7 × 7 × 7 × 7 = 16807.

So, the numerical equivalent of 7^2⋅7^3 is 16807.
Answered by GPT 3.5
To find the numerical equivalent of 3^9⋅3^(-5), we can simplify the expression by applying the product rule of exponents. According to this rule, when multiplying two numbers with the same base, we add their exponents.

So, 3^9⋅3^(-5) can be written as 3^(9 + (-5)) = 3^4.

To find the numerical value of 3^4, we calculate it as follows:

3^4 = 3 × 3 × 3 × 3 = 81.

Thus, the numerical equivalent of 3^9⋅3^(-5) is 81.
Answered by GPT 3.5
The expression that is correctly developed to use the Product Rule of Exponents is 62⋅73, which means 6 squared times 7 cubed.
Answered by GPT 3.5
Apologies for the confusion. You are correct, none of the given options are correctly developed to use the Product Rule of Exponents.
Answered by GPT 3.5
Apologies for the confusion. Based on the given options, the expression that is correctly developed to use the Product Rule of Exponents is (52)9, which means (5 squared) to the power of 9.
Answered by GPT 3.5
Apologies for the incorrect response earlier. No, the expression (52)9 is not correctly developed to use the Product Rule of Exponents. The correct expression to use the Product Rule of Exponents would be 62⋅73, which represents 6 squared times 7 cubed.
Answered by GPT 3.5
To simplify the expression 100^8⋅100^7 using the Product Rule of Exponents, we add the exponents:

100^8⋅100^7 = 100^(8+7) = 100^15.

Therefore, the correct answer is 100^15.
Answered by GPT 3.5
To find the numerical equivalent of 102 ⋅ 103, we need to simplify the expression by applying the product rule of exponents. According to this rule, when multiplying two numbers with the same base, we add their exponents.

So, 102 ⋅ 103 can be written as 10(2 + 3) = 105.

Therefore, the numerical equivalent of 102 ⋅ 103 is 105.
Answered by GPT 3.5
To find the numerical equivalent of 25 ⋅ 2^(-2), we can simplify the expression by applying the product rule of exponents. According to this rule, when multiplying two numbers with the same base, we add their exponents.

In this case, we have 2^(-2), which means we need to take the reciprocal of 2^2.

2^2 = 2 × 2 = 4.

Taking the reciprocal, we have 1/4.

So, 25 ⋅ 2^(-2) = 25 × 1/4 = 25/4 = 6.25.

Therefore, the numerical equivalent of 25 ⋅ 2^(-2) is 6.25.
Answered by GPT 3.5
Apologies for the mistake. Let's correct it.

To find the numerical equivalent of 25 ⋅ 2^(-2), we need to simplify the expression.

First, let's calculate 2^(-2). Using the product rule of exponents, we know that a negative exponent indicates taking the reciprocal of the number with a positive exponent. So, 2^(-2) = 1/(2^2) = 1/4.

Now, we can rewrite the expression as 25 ⋅ (1/4). To multiply fractions, we multiply the numerators together and the denominators together:

25 ⋅ (1/4) = 25/1 ⋅ 1/4 = 25/4 = 6.25.

Therefore, the numerical equivalent of 25 ⋅ 2^(-2) is 6.25.
Answered by GPT 3.5
To find the numerical equivalent of 2^5 ⋅ 2^(-2), we can simplify the expression by applying the product rule of exponents. According to this rule, when multiplying two numbers with the same base, we add their exponents.

So, 2^5 ⋅ 2^(-2) can be written as 2^(5 + (-2)) = 2^3.

To evaluate 2^3, we simply multiply 2 three times:

2^3 = 2 × 2 × 2 = 8.

Therefore, the numerical equivalent of 2^5 ⋅ 2^(-2) is 8.
Answered by GPT 3.5
To simplify the expression 4^9 times 4^(-7), we can apply the product rule of exponents. The product rule states that when multiplying two numbers with the same base, we add the exponents.

So, 4^9 times 4^(-7) can be written as 4^(9 + (-7)) = 4^2.

To evaluate 4^2, we multiply 4 by itself:

4^2 = 4 × 4 = 16.

Therefore, the numerical equivalent of 4^9 times 4^(-7) is 16.