Use the Product Rule of Exponents to simplify the expression 24 ⋅22

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To simplify the expression using the Product Rule of Exponents, we add the exponents when multiplying two numbers with the same base.

In this case, the base is 2.

So, 24 ⋅ 22 = 2^4 ⋅ 2^2

Using the Product Rule of Exponents, we add the exponents:

2^4 ⋅ 2^2 = 2^(4+2) = 2^6

Therefore, 24 ⋅ 22 simplified using the Product Rule of Exponents is 2^6.

Use the Product Rule of Exponents to simplify the expression 38 ⋅33

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To simplify the expression using the Product Rule of Exponents, we add the exponents when multiplying two numbers with the same base.

In this case, the base is 3.

So, 38 ⋅ 33 = 3^8 ⋅ 3^3

Using the Product Rule of Exponents, we add the exponents:

3^8 ⋅ 3^3 = 3^(8+3) = 3^11

Therefore, 38 ⋅ 33 simplified using the Product Rule of Exponents is 3^11.

Use the Product Rule of Exponents to simplify the expression 75 ⋅72

To use the Product Rule of Exponents to simplify the expression 75 ⋅ 72, we need to determine the common base. In this case, the common base is 7.

So, 75 ⋅ 72 = 7^5 ⋅ 7^2.

Using the Product Rule of Exponents, we add the exponents:

7^5 ⋅ 7^2 = 7^(5+2) = 7^7.

Therefore, 75 ⋅ 72 simplified using the Product Rule of Exponents is 7^7.

Find the numerical equivalent of 72⋅

I apologize for the incomplete response in my previous message.

To find the numerical equivalent of 72, we need to specify the exponent. Assuming you meant 72^0, we can evaluate this expression as follows:

72^0 = 1.

Therefore, the numerical equivalent of 72^0 is 1.

Which expression is correctly developed to use the Product Rule of Exponents?(1 point)

Responses

62⋅73
6 squared times 7 cubed

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

327
32 superscript 7 baseline

108⋅108

The expression that is correctly developed to use the Product Rule of Exponents is:

108⋅108

Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008⋅1007?(1 point)

Responses

20015
200 superscript 15 baseline

10015
100 superscript 15 baseline

10,00015
10,000 superscript 15 baseline

10056

To use the Product Rule of Exponents to simplify the expression 1008⋅1007, we need to add the exponents of the common base (10).

The only option that is correctly simplified using the Product Rule of Exponents is:

10015

Find the numerical equivalent of 102 ⋅103(1 point)

Responses

1,100
1,100

100,000
100,000

105
10 superscript 5 baseline

10

To find the numerical equivalent of 102 ⋅ 103, we need to multiply the two numbers together.

102 ⋅ 103 = 100 ⋅ 1,000 = 100,000

Therefore, the numerical equivalent of 102 ⋅ 103 is 100,000.

Find the numerical equivalent of 25 ⋅2−2(1 point)

Responses

16
16

8
8

128
128

2

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

Recall that a negative exponent means taking the reciprocal of the base raised to the positive exponent.

2^(-2) = 1/2^2 = 1/4

Now we can multiply:

25 ⋅ (1/4) = 25/4 = 6.25

Therefore, the numerical equivalent of 25 ⋅ 2^(-2) is 6.25.

Find the numerical equivalent of 49⋅4−7(1 point)

Responses

4
4

42
4 squared

16
16

416

To find the numerical equivalent of 49⋅4^(-7), we need to evaluate the expression.

Recall that a negative exponent means taking the reciprocal of the base raised to the positive exponent.

4^(-7) = 1/4^7 = 1/16384

Now we can multiply:

49⋅(1/16384) = 49/16384 ≈ 0.00299

Therefore, the numerical equivalent of 49⋅4^(-7) is approximately 0.00299.