Find the numerical equivalent of 99⋅9−6
The numerical equivalent of 99⋅9−6 is 992.
Find the numerical equivalent of 9^9⋅9^−6
The numerical equivalent of 9^9⋅9^−6 is 9^3, which is equal to 729.
What is the missing exponent in the following equation?
h^450/h"^? = h^215
To find the missing exponent, we can set up an equation using the properties of exponents.
We have h^450 / h^? = h^215
Using the quotient property of exponents, we subtract the exponents when dividing. Therefore, we can rewrite the equation as:
h^(450 - ?) = h^215
To find the missing exponent, we set the exponents equal to each other:
450 - ? = 215
To solve for ?, we isolate the variable:
? = 450 - 215
? = 235
Therefore, the missing exponent is 235.
Simplify 1287÷1225 .(1 point)
To simplify 1287 ÷ 1225, we divide the numerator (1287) by the denominator (1225).
1287 ÷ 1225 = 1.05
Therefore, 1287 ÷ 1225 simplifies to 1.05.
What is the missing number in this simplified exponential expression: 7?÷75=712 ?
To find the missing number in the simplified exponential expression, we need to solve for the missing exponent.
The given equation is: 7? ÷ 75 = 712
To find the missing exponent, we can rewrite the equation using the properties of exponents. The denominator can be written as 7^2.
Therefore, the equation becomes: 7? ÷ 7^2 = 712
Now, we can simplify the left side of the equation by using the quotient property of exponents. We subtract the exponents when dividing:
7^(? - 2) = 712
We can solve for the missing exponent by equating the exponents on both sides:
? - 2 = 12
To find the value of ?, we isolate the variable:
? = 12 + 2
? = 14
Therefore, the missing number in the simplified exponential expression is 14.
Apply the Zero Power Rule to create an equivalent expression to 9⋅(−33)0+32(8−270).(2 points)
9⋅(−33)0+32(8−270) =
⋅
+32(
–
)
When applying the Zero Power Rule, any non-zero number raised to the power of zero is equal to 1. Therefore, (-33)^0 is equal to 1.
Using this rule, we can simplify the expression:
9⋅(-33)^0 + 32(8 - 270) = 9⋅1 + 32(-262)
Simplifying further:
9 + (-8384) = -8375
Therefore, 9⋅(−33)0 + 32(8−270) simplifies to -8375.
9⋅(−33)0+32(8−270) =
⋅
+32(
–
)
9⋅(−33)0 + 32(8−270) can be written as:
9⋅1 + 32(-262)
Simplifying the expression further:
9 + (-8384) = -8375.
Therefore, 9⋅(−33)0 + 32(8−270) simplifies to -8375.
Apply the Property of Negative Integer Exponents to solve 7^−3 . The answer should not contain any exponent expression or decimals.(1 point)
7^−3 =
By applying the property of negative integer exponents, we can rewrite 7^-3 as the reciprocal of 7^3:
7^-3 = 1 / 7^3
Since 7^3 is equal to 343, the reciprocal of 343 is:
1 / 343
Therefore, 7^-3 simplifies to 1 / 343.
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3−178−14 with positive exponents only.(1 point)
3^−17/8^−14 =
To apply the property of negative integer exponents, we can rewrite the expression as the reciprocal:
3^-17 / 8^-14 = 1 / (3^17 * 8^14)
Next, we can convert the negative exponents to positive exponents by taking the reciprocal of the base:
1 / (3^17 * (1/8)^14)
Simplifying further:
1 / (3^17 * (1^14 / 8^14))
Since any number raised to the power of one is itself, 1^14 is equal to 1.
1 / (3^17 / 8^14)
Using the rule for dividing exponents with the same base, subtract the exponents:
1 / (8^14 / 3^17)
Multiplying by the reciprocal is the same as dividing, so we can rewrite the expression as:
3^17 / 8^14
Therefore, 3^-17 / 8^-14 is equivalent to 3^17 / 8^14 with positive exponents only.
Apply the Properties of Integer Exponents to generate equivalent expressions to (7−3)7 ⋅ 7206−2 with only positive exponents, then solve the expression. Provide the answer as an improper fraction.(1 point)
(7^−3)^7 ⋅ 7^20/6^−2 =
To simplify the expression (7^-3)^7 ⋅ 7^20/6^-2, we can apply the properties of integer exponents.
First, we simplify the expression inside the parentheses using the power of a power property:
(7^-3)^7 = 7^(-3 * 7) = 7^-21
Next, we simplify the expression:
7^-21 ⋅ 7^20/6^-2
Since the bases are the same (7), we can add the exponents:
7^(-21 + 20)/6^-2
7^(-1)/6^-2
To get rid of the negative exponents, we can rewrite the expression with positive exponents by taking the reciprocal of the base:
1/7^1 * 6^2
1/7 * 6^2
Finally, we can calculate the value of the expression:
1/7 * 6^2 = 1/7 * 36 = 36/7
Therefore, the simplified expression (7^-3)^7 ⋅ 7^20/6^-2 is equal to 36/7 as an improper fraction.
Apply the product rule of integer exponents to find the numerical equivalent of 12−5⋅127 . Show your work and explain how you used the product rule of integer exponents.
To find the numerical equivalent of 12^-5⋅12^7, we can use the product rule of integer exponents.
The product rule states that when multiplying expressions with the same base, we can add the exponents.
First, let's simplify the expression:
12^-5⋅12^7
Using the product rule of exponents, we add the exponents:
12^(-5 + 7)
Simplifying further:
12^2
Now, we calculate the value of 12^2:
12^2 = 12 * 12 = 144
Therefore, the numerical equivalent of 12^-5⋅12^7 is 144.