Question
Use the Product Rule of Exponents to simplify 5^10⋅5^5
Answers
Answer
Find the numerical equivalent of 9^9⋅9^−6
Answer
What is the missing exponent in the following equation?
h^450/h^? = h^215
h^450/h^? = h^215
Answer
Simplify 12^87÷12^25.
Answered by
GPT 3.5
To simplify 5^10 * 5^5 using the Product Rule of Exponents, we add the exponents when the bases are the same. Therefore, we can simplify this expression as 5^(10 + 5) = 5^15.
Answered by
GPT 3.5
To find the numerical equivalent of 9^9 * 9^-6, we use the Product Rule of Exponents and evaluate the exponents separately.
First, we know that 9^9 = 387,420,489 (by multiplying 9 by itself 9 times).
Second, we know that 9^-6 = 1/(9^6) = 1/531,441 (by taking the reciprocal of 9^6, which is obtained by multiplying 9 by itself 6 times and then inverting the result).
Therefore, the numerical equivalent of 9^9 * 9^-6 is 387,420,489 * 1/531,441 = 0.728.
First, we know that 9^9 = 387,420,489 (by multiplying 9 by itself 9 times).
Second, we know that 9^-6 = 1/(9^6) = 1/531,441 (by taking the reciprocal of 9^6, which is obtained by multiplying 9 by itself 6 times and then inverting the result).
Therefore, the numerical equivalent of 9^9 * 9^-6 is 387,420,489 * 1/531,441 = 0.728.
Answered by
GPT 3.5
To find the missing exponent, we use the Quotient Rule of Exponents.
According to the Quotient Rule, when dividing two numbers with the same base, we subtract the exponent of the denominator from the exponent of the numerator.
In this case, we have h^450/h^x = h^215.
Applying the Quotient Rule, we subtract the exponent "x" from the exponent 450: 450 - x = 215.
To find the value of "x", we solve the equation: 450 - x = 215.
Subtracting 450 from both sides of the equation, we have -x = 215 - 450.
Simplifying, we get: -x = -235.
Finally, multiplying both sides of the equation by -1, we get x = 235.
Therefore, the missing exponent in the equation h^450/h^x = h^215 is x = 235.
According to the Quotient Rule, when dividing two numbers with the same base, we subtract the exponent of the denominator from the exponent of the numerator.
In this case, we have h^450/h^x = h^215.
Applying the Quotient Rule, we subtract the exponent "x" from the exponent 450: 450 - x = 215.
To find the value of "x", we solve the equation: 450 - x = 215.
Subtracting 450 from both sides of the equation, we have -x = 215 - 450.
Simplifying, we get: -x = -235.
Finally, multiplying both sides of the equation by -1, we get x = 235.
Therefore, the missing exponent in the equation h^450/h^x = h^215 is x = 235.
Answered by
GPT 3.5
To simplify 12^87 ÷ 12^25, we use the Quotient Rule of Exponents. According to the Quotient Rule, when dividing two numbers with the same base, we subtract the exponent of the denominator from the exponent of the numerator.
In this case, we have 12^87 ÷ 12^25.
Applying the Quotient Rule, we subtract the exponent 25 from the exponent 87: 87 - 25 = 62.
So, 12^87 ÷ 12^25 simplifies to 12^62.
In this case, we have 12^87 ÷ 12^25.
Applying the Quotient Rule, we subtract the exponent 25 from the exponent 87: 87 - 25 = 62.
So, 12^87 ÷ 12^25 simplifies to 12^62.