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