Question

Use the Product Rule of Exponents to simplify 5^{10}\cdot5^5
Answer
What is the missing exponent in the following equation? \frac{h^{450}}{h^?}\ =\ h^{215}
Answer
Simplify 12^{87}\div12^{25}
Answer
What is the value of 6.9-2^0
Answer
Apply the Zero Power Rule to create an equivalent expression to 9\cdot(-33)^0+\frac{3}{2}(8-27^0)
Answer
this is the answer btw people 9 * 1 + (3/2) * (8 - 1)
Answer
Solve the expression \frac{15\cdot8^0}{5}+4\left(7^0-6\right)
Answer
Use the Power Rule of Exponents to simplify (10^3)^6
Answer
If the expression 7^{15} was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?
Answered by ablockofcheese
thx man. ur the best. helped me alot with my test @Anonymous
Answered by ablockofcheese
even tho the bot was wrong on a couple of questions.
Answered by dsads
what are the answers to all?
Answered by some furry or something like that :3
the test has 15 questions and this chain only covers 8 of them please help
Answered by 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.
Answered by 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.
Answered by 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
Answered by 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.
Answered by 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.
Answered by 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.
Answered by 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.
Answered by 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.
Answered by 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