Question

Use the Product Rule of Exponents to simplify 5^{10}\cdot5^5

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the expression 5^10 * 5^5 using the Product Rule of Exponents, we add the exponents when we multiply two exponential expressions with the same base.

5^10 * 5^5 = 5^(10+5)
5^10 * 5^5 = 5^15

Therefore, the simplified form of 5^10 * 5^5 is 5^15.

Answer 2

What is the missing exponent in the following equation? \frac{h^{450}}{h^?}\ =\ h^{215}

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the missing exponent in the equation h^450 / h^? = h^215, we use the quotient rule of exponents. According to this rule, when we divide two exponential expressions with the same base, we subtract the exponents.

Therefore, the missing exponent is:

450 - ? = 215

To solve for ?, we subtract both sides of the equation by 450:

? = 450 - 215

Simplifying the right side gives:

? = 235

So, the missing exponent in the equation is 235.

Answer 4

Simplify 12^{87}\div12^{25}

Answer 5

[AI-generated answer — Bot GPT 3.5]

To simplify 12^87 ÷ 12^25, we can use the Quotient Rule of Exponents which states that when dividing two exponential expressions with the same base, we subtract the exponents.

Therefore, 12^87 ÷ 12^25 can be simplified as 12^(87-25):

12^87 ÷ 12^25 = 12^(87-25)

To calculate the exponent 87 - 25, we get:

87 - 25 = 62

Therefore, 12^87 ÷ 12^25 simplifies to:

12^87 ÷ 12^25 = 12^62

Answer 6

What is the value of 6.9-2^0

Answer 7

[AI-generated answer — Bot GPT 3.5]

The value of 6.9 - 2^0 can be calculated as follows:

Since any number raised to the power of 0 is equal to 1, 2^0 equals 1.

Therefore, 6.9 - 2^0 becomes 6.9 - 1.

Subtracting 1 from 6.9, we find:

6.9 - 1 = 5.9.

So, the value of 6.9 - 2^0 is 5.9.

Answer 8

Apply the Zero Power Rule to create an equivalent expression to 9\cdot(-33)^0+\frac{3}{2}(8-27^0)

Answer 9

[AI-generated answer — Bot GPT 3.5]

The Zero Power Rule states that any nonzero number raised to the power of 0 is equal to 1. Applying this rule to the given expression, we have:

9 * (-33)^0 + (3/2) * (8 - 27^0)

Since any number raised to the power of 0 is equal to 1, (-33)^0 is equal to 1, and 27^0 is also equal to 1.

Therefore, the expression simplifies to:

9 * 1 + (3/2) * (8 - 1)

The parentheses can be simplified:

9 + (3/2) * 7

Now, we can multiply:

9 + 21/2

To add the fractions, we need a common denominator:

(18/2) + (21/2) = 39/2

So, the equivalent expression is 39/2.

Answer 10

this is the answer btw people 9 * 1 + (3/2) * (8 - 1)

Answer 11

[AI-generated answer — Bot GPT 3.5]

Apologies for the confusion in the previous response. Let's simplify the expression correctly:

9 * 1 + (3/2) * (8 - 1)

Since any number raised to the power of 0 is equal to 1, (-33)^0 and 27^0 both become 1. So the expression becomes:

9 * 1 + (3/2) * (8 - 1)

Simplifying the parentheses first:

9 * 1 + (3/2) * (7)

Next, we multiply the fractions:

9 + (21/2)

To add the fractions, we need a common denominator:

(18/2) + (21/2) = 39/2

Therefore, the correct simplified expression is 39/2.

Answer 12

Solve the expression \frac{15\cdot8^0}{5}+4\left(7^0-6\right)

Answer 13

[AI-generated answer — Bot GPT 3.5]

Let's solve the expression step by step:

First, we can simplify 8^0 since any number raised to the power of 0 is equal to 1:

\frac{15\cdot8^0}{5}+4\left(7^0-6\right)

\frac{15\cdot1}{5}+4\left(7^0-6\right)

Next, we can simplify 7^0 since any number raised to the power of 0 is equal to 1:

\frac{15}{5}+4\left(1-6\right)

Simplifying further:

3 + 4(-5)

Multiplying 4 by -5:

3 + (-20)

Finally, adding the numbers:

3 - 20 = -17

Therefore, the solution to the expression is -17.

Answer 14

Use the Power Rule of Exponents to simplify (10^3)^6

Answer 15

[AI-generated answer — Bot GPT 3.5]

The Power Rule of Exponents states that when raising an exponential expression to another exponent, we multiply the exponents.

Therefore, we can simplify (10^3)^6 as follows:

(10^3)^6 = 10^(3*6)

Multiplying the exponents:

10^(18)

So, the simplified form of (10^3)^6 is 10^18.

Answer 16

If the expression 7^{15} was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?

Answer 17

[AI-generated answer — Bot GPT 3.5]

If the expression 7^{15} was simplified using the Power Rule of Exponents, the expanded equivalent expression would be:

7^15 = 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7

Answer 18

thx man. ur the best. helped me alot with my test @Anonymous

Answer 19

even tho the bot was wrong on a couple of questions.

Answer 20

what are the answers to all?

Answer 21

the test has 15 questions and this chain only covers 8 of them please help