Use the product rule of exponents simplify 3^5 * 3^7
To simplify the expression, we can apply the product rule of exponents, which states that when multiplying two exponential expressions with the same base, you can add their exponents.
3^5 * 3^7 = 3^(5+7) = 3^12
Therefore, 3^5 * 3^7 simplifies to 3^12.
find the numerical equivalent of 5^10 * 5^-6
To find the numerical equivalent of 5^10 * 5^-6, we can simplify the expression using the product rule of exponents and then compute the result.
Using the product rule, we add the exponents of the same base:
5^10 * 5^-6 = 5^(10 + (-6)) = 5^4
Therefore, 5^10 * 5^-6 is equal to 5^4.
Now, let's evaluate 5^4:
5^4 = 5 * 5 * 5 * 5 = 625
So, the numerical equivalent of 5^10 * 5^-6 is 625.
What is the missing exponent in the following equation?
8^500 / 8^? = s^175
To find the missing exponent in the equation 8^500 / 8^? = s^175, we can apply the quotient rule of exponents.
The quotient rule states that when dividing exponential expressions with the same base, you subtract their exponents.
So, in this case, we have:
8^500 / 8^? = s^175
Using the quotient rule, we can subtract the exponent of 8 on the right side of the equation from the exponent on the left side:
8^500 / 8^? = s^175
8^(500 - ?) = s^175
To find the missing exponent, we need to match the exponents on the left and right sides of the equation. Since 8^500 is not equal to s^175, there is no specific value for the missing exponent that will make the equation true.
What is the missing exponent in the following equation? s^500/s^?=s^175
To find the missing exponent in the equation s^500 / s^? = s^175, we can apply the quotient rule of exponents.
The quotient rule states that when dividing exponential expressions with the same base, you subtract their exponents.
So, in this case, we have:
s^500 / s^? = s^175
Using the quotient rule, we can subtract the exponent of s on the right side of the equation from the exponent on the left side:
s^(500 - ?) = s^175
To find the missing exponent, we need to match the exponents on the left and right sides of the equation.
Since the bases are the same (s), in order for the equation to be true, the exponents must also be equal:
500 - ? = 175
To find the missing exponent (?), we can subtract 175 from 500:
500 - ? = 175
? = 500 - 175
? = 325
Therefore, the missing exponent in the equation s^500 / s^? = s^175 is 325.
What is the missing number in this simplified exponential expression:
8^? / 8^4 = 8^15?
To find the missing number in the equation 8^? / 8^4 = 8^15?, we can apply the quotient rule of exponents.
The quotient rule states that when dividing exponential expressions with the same base, you subtract their exponents.
So, in this case, we have:
8^? / 8^4 = 8^15?
Using the quotient rule, we can subtract the exponent of 8 on the right side of the equation from the exponent on the left side:
8^(? - 4) = 8^15?
To find the missing number, we need to match the exponents on the left and right sides of the equation.
Since the base is the same (8), in order for the equation to be true, the exponents must also be equal:
? - 4 = 15?
To solve for the missing number (?), we can subtract 15? from both sides:
? - 15? = 4
Combining like terms:
-14? = 4
Dividing both sides by -14:
? = 4 / -14
Simplifying:
? = -2/7
Therefore, the missing number in the equation 8^? / 8^4 = 8^15? is -2/7.
What is the missing number in this simplified exponential expression:
8^? / 8^4 = 8^15