What is the missing exponent in the following equation? h^450/h? = h^215 (1 point)
The missing exponent in the equation is 235.
Simplify 12^87 divided by 12^25
To simplify the expression 12^87 divided by 12^25, subtract the exponents:
12^(87 – 25) = 12^62
what is the value of 6.0 - 2^0
4.9
5.9
7.9
6.9
The value of 6.0 - 2^0 is 5.0. None of the answer choices provided is correct.
what is the value of 6.9 - 2^0
4.9
5.9
7.9
6.9
The value of 6.9 - 2^0 is 5.9. Therefore, the correct answer is 5.9.
apply the zero power rule to create an equivalent expression to 9 x ( -33 )^0 + 3/2 ( 8 - 2 27^0 )
9 x (-33)^0 + 3/2 ( 8 - 27^0 ) = blank * blank + 3/2 ( blank - blank )
Applying the zero power rule, any non-zero number raised to the power of 0 is equal to 1. Therefore, we have:
9 x (-33)^0 + 3/2 ( 8 - 27^0 ) = 9 x 1 + 3/2 ( 8 - 1 )
We can simplify this further:
= 9 + 3/2 ( 7 )
= 9 + 21/2
This can be written as:
9 + 10.5
Therefore, the equivalent expression is:
9 + 10.5 + 3/2 ( 8 - 1 )
solve the expression 15-8^0/5 + 4 ( 7^0 - 6 )
To solve the expression 15 - 8^0/5 + 4(7^0 - 6), we follow the order of operations (parentheses, exponents, multiplication/division, addition/subtraction):
First, we evaluate the exponent 8^0, which is equal to 1.
Now we can substitute this value back into the original expression:
15 - 1/5 + 4(1 - 6)
Next, we simplify within the parentheses:
15 - 1/5 + 4(-5)
Now, multiply 4 by -5:
15 - 1/5 - 20
We can rewrite 15 as a fraction with a common denominator of 5:
75/5 - 1/5 - 20
Now combine the fractions:
(75 - 1)/5 - 20
Simplify the numerator:
74/5 - 20
To combine these fractions, we need to find a common denominator. Multiplying 20 by 5 gives us 100:
74/5 - 100/5
Now we can combine the fractions:
(74 - 100)/5
Simplify the numerator:
-26/5
Therefore, the solution to the expression 15 - 8^0/5 + 4(7^0 - 6) is -26/5 or -5.2.
use the power rule of exponents to simplify (10^3)^6
To simplify (10^3)^6 using the power rule of exponents, we multiply the exponents:
(10^3)^6 = 10^(3*6) = 10^18
Therefore, (10^3)^6 simplifies to 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?
( 7 x 7 x 7 x 7 x 7 )^10
( 7 x 7 x 7 ) x ( 7 x 7 x 7 ) x ( 7 x 7 x 7 ) x ( 7 x 7 x 7 ) x ( 7 x 7 x 7 )
( 7^18)^3
( 7^10)^5
The correct expanded equivalent expression when simplifying 7^15 using the power rule of exponents would be (7 x 7 x 7 x 7 x 7)^10.
Therefore, the correct choice is:
( 7 x 7 x 7 x 7 x 7 )^10
use the power rule of exponents to create a simplified equivalent expression for ( 19^4)^9
To create a simplified equivalent expression for (19^4)^9 using the power rule of exponents, we multiply the exponents:
(19^4)^9 = 19^(4*9) = 19^36
Therefore, the simplified equivalent expression for (19^4)^9 is 19^36.
apply the property of negative integer exponents to solve 7^-3. the answer should not contain any exponent expression or decimals.
Applying the property of negative integer exponents, we know that:
a^(-n) = 1/(a^n)
Therefore, for 7^-3:
7^-3 = 1/(7^3)
Simplifying further:
7^3 = 7 x 7 x 7 = 343
Thus, 7^-3 = 1/343.
apply the property of negative integer exponents to generate an expression equivalent to 3^-17/8^-14 with positive exponents only
Applying the property of negative exponents, we can rewrite 3^-17 as 1/3^17 and 8^-14 as 1/8^14.
Therefore, the expression 3^-17/8^-14 can be rewritten as (1/3^17)/(1/8^14).
To simplify this further, we can multiply the numerator and denominator by the reciprocal of the denominator, which is 8^14/1.
This gives us (1/3^17) * (8^14/1).
Now, we can simplify the expression using positive exponents:
(8^14)/(3^17).
So, an expression equivalent to 3^-17/8^-14 with positive exponents only is (8^14)/(3^17).
apply the properties of integer exponents to generate equivalent expressions to ( 7^-3)^7 x 7^20/ 6^-2 with only positive exponents, then solve the expression. provide the answer as an improper fraction
Applying the properties of integer exponents, we can simplify the expression (7^-3)^7 x (7^20)/6^-2 with only positive exponents.
First, let's simplify the exponent (7^-3)^7. Using the property (a^m)^n = a^(m*n), we have:
(7^-3)^7 = 7^(-3*7) = 7^-21
Next, we simplify the exponent 6^-2. Using the property a^(-n) = 1/(a^n), we have:
6^-2 = 1/(6^2) = 1/36
Now we can rewrite the expression with positive exponents:
(7^-21) x (7^20)/6^-2 = (1/7^21) x (7^20)/(1/36)
Using the property of division, division of two fractions can be simplified to a multiplication by the reciprocal of the divisor:
(1/7^21) x (7^20) x (36/1)
Now, we use the property a^m x a^n = a^(m+n):
(1/7^21) x (7^20) x (36/1) = (1 x 7^20 x 36) / (7^21 x 1)
Simplifying the numerator and denominator separately:
7^20 x 36 = 7^(20+2) = 7^22
7^21 x 1 = 7^21
Now we have:
(7^22) / (7^21)
Using the property a^m / a^n = a^(m-n):
(7^22) / (7^21) = 7^(22-21) = 7^1
Therefore, the solution to the expression is 7 as an improper fraction: 7/1.
simplify the expression ( 4x^3 )^2 using properties of integer exponents
4x^6
8x^6
16x^5
16x^6
To simplify the expression (4x^3)^2 using properties of integer exponents, we apply the power rule of exponents, which states that (a^m)^n = a^(m*n).
In this case, we have (4x^3)^2, where 4 and x^3 are the base and 2 is the exponent.
Applying the power rule, we have:
(4x^3)^2 = 4^(2*1) * (x^3)^(2*1)
Simplifying:
= 4^2 * x^(3*2)
= 16x^6
Therefore, the simplified expression is 16x^6.
apply the properties of integer exponents to generate an equivalent algebraic expression to (4x^4y^-4)^3/(x^7y^3)^2
64/x^20
4/x^2y^18
x^2y^18/64
64/x^2y^18
To generate an equivalent algebraic expression for (4x^4y^-4)^3/(x^7y^3)^2 using the properties of integer exponents, we'll apply the power and division rules of exponents.
First, let's simplify the numerator: (4x^4y^-4)^3
Using the power rule of exponents, we raise each term inside the parentheses to the power of 3:
4^3 * (x^4)^3 * (y^-4)^3
Simplifying the exponents:
64 * x^(4*3) * y^(-4*3)
64 * x^12 * y^(-12)
Now, let's simplify the denominator: (x^7y^3)^2
Using the power rule of exponents, we raise each term inside the parentheses to the power of 2:
(x^7)^2 * (y^3)^2
x^(7*2) * y^(3*2)
x^14 * y^6
Therefore, the expression becomes:
(64 * x^12 * y^(-12))/(x^14 * y^6)
Using the division rule of exponents, we subtract the exponents of the common bases:
64 * x^(12 - 14) * y^(-12 - 6)
64 * x^(-2) * y^(-18)
Finally, we can rewrite this in a positive exponential form:
64/(x^2y^18)
Therefore, the equivalent algebraic expression to (4x^4y^-4)^3/(x^7y^3)^2 is 64/(x^2y^18).
apply the product rule of integer exponents to find the numerical equivalent of 12^-5 x 12^7. show your work and explain how you used the product rule of integer exponents
The product rule of integer exponents states that when multiplying two numbers with the same base, we add their exponents.
In this case, we have 12^-5 x 12^7, and since both terms have the base 12, we can apply the product rule by adding their exponents.
12^-5 x 12^7 = 12^(-5 + 7)
Now let's simplify the exponent:
-5 + 7 = 2
Therefore, 12^-5 x 12^7 simplifies to 12^2.
To calculate the numerical value, we can evaluate 12^2:
12^2 = 12 x 12 = 144
So, the numerical equivalent of 12^-5 x 12^7 is 144.