simplify 12^87 divided by 12^25
To simplify this expression, we can subtract the exponents of 12.
12^87 divided by 12^25 is equivalent to 12^(87-25) which is equal to 12^62.
what is the missing number in this simplified exponential expression: 7^? divided by 7^5 = 7^12?
To find the missing number, we can equate the exponents of 7.
We have 7^? divided by 7^5 equal to 7^12.
Using the quotient rule of exponents, we subtract the exponents because the bases are the same:
7^(? - 5) = 7^12.
To maintain equality, the exponents should be the same, so:
? - 5 = 12.
Adding 5 to both sides of the equation, we get:
? = 17.
Therefore, the missing number is 17.
what is the value of 6.9 - 2^0?
Any number raised to the power of 0 is equal to 1. Therefore, 2^0 = 1.
To find the value of 6.9 - 2^0, we substitute 2^0 with 1:
6.9 - 1 = 5.9.
Therefore, the value of 6.9 - 2^0 is 5.9.
apply the zero power rule to create an equivalent expression to 9*(-33)^0 + 3/2 (8 - 27^0)
9*(-33)^0 + 3/2 (8 - 27^0) = _____ * _____ + 3/2 (____ - _____)
Applying the zero power rule, any non-zero number raised to the power of 0 is equal to 1. Therefore:
9*(-33)^0 = 9 * 1 = 9
And:
27^0 = 1
Now, substituting these values into the expression:
9*(-33)^0 + 3/2 (8 - 27^0) = 9 * 1 + 3/2 (8 - 1)
The expression becomes:
(9 * 1) + 3/2 (8 - 1) = 9 + 3/2 (7)
Therefore, the equivalent expression is:
9 + 3/2 (7).
solve the expression 15*8^0/5 + 4 (7^0 - 6)
Using the zero power rule, any non-zero number raised to the power of 0 is equal to 1. Therefore, 8^0 = 1 and 7^0 = 1.
Now we can solve the expression:
15*8^0/5 + 4 (7^0 - 6)
= 15*1/5 + 4 (1 - 6)
= 15/5 + 4 (-5)
Simplifying further:
= 3 + 4 (-5)
= 3 - 20
= -17
Therefore, the value of the expression 15*8^0/5 + 4 (7^0 - 6) is -17.
use the power rule of exponents to simplify (10^3)^6
Using the power rule of exponents, we multiply the exponents when raising a power to a power.
(10^3)^6 = 10^(3*6)
Multiplying the exponents, we get:
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
If the expression 7^15 was simplified using the power rule of exponents, the expanded equivalent expression would be:
7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7
y = 4x - 3
The given equation is y = 4x - 3. This equation represents a linear relationship between the variables x and y.
In this equation, the coefficient of x is 4, which represents the slope of the line. The slope indicates how much y changes for each unit increase in x.
The equation also has a constant term of -3, which represents the y-intercept. The y-intercept is the point where the line intersects the y-axis when x is equal to 0.
So, the equation y = 4x - 3 describes a line with a slope of 4 and a y-intercept of -3.
apply the property of negative integer exponents to solve 7^-3. the answer should not contain any exponent expression or decimals
To solve 7^-3 using the property of negative exponents, we can rewrite it as:
1 / 7^3
Since 7^3 is equal to 7 * 7 * 7 = 343, the expression becomes:
1 / 343
Therefore, the value of 7^-3 is 1/343.
are you sure thats correct
Apologies for the mistake.
To correctly solve 7^-3 using the property of negative exponents, we can reciprocate the base and change the sign of the exponent, resulting in:
1 / 7^3 = 1 / (7 * 7 * 7) = 1 / 343
So, the correct value of 7^-3 is indeed 1/343.
apply the property of negative integer exponents to generate an expression equivalent to 3^-17/8^-14 with positive exponents only
To generate an expression equivalent to 3^-17/8^-14 with positive exponents only, we can apply the property of negative exponents by reciprocating the base and changing the sign of the exponent.
In this case, we have:
3^-17/8^-14
Reciprocating the bases gives:
8^14/3^17
Therefore, the 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 * 7^20/6^-2 with only positive exponents, then solve the expression. provide the answer as an improper fraction
To generate equivalent expressions with only positive exponents, we can apply the property of negative exponents by reciprocating the base and changing the sign of the exponent.
Starting with (7^-3)^7, we can rewrite it as (1/7^3)^7:
(1/7^3)^7 * 7^20/6^-2
This simplifies to (1^7/7^(3*7)) * 7^20/6^-2:
1/7^21 * 7^20/6^-2
Then we can rewrite 6^-2 as the reciprocal with 2 positive exponent: 1/6^2:
1/7^21 * 7^20/1/6^2
Now, let's simplify the expression:
1/7^21 * 7^20 * 6^2
Using the property of exponents, we can add the exponents when multiplying with the same base:
1/7^(21-20) * 6^2
Therefore, the final equivalent expression is 1/7 * 6^2.
Now, we can solve the expression:
1/7 * 6^2 = 1/7 * 36
Calculating the multiplication:
1/7 * 36 = 36/7
So, the answer is 36/7, which is an improper fraction.
apply the product rule of integer exponents to find the numerical equivalent of 12^-5 * 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 expressions with the same base, we can add their exponents.
In this case, we have 12^-5 * 12^7.
According to the product rule, we can add the exponents (-5 + 7) and keep the base 12 the same.
So, 12^-5 * 12^7 simplifies to 12^2.
Now, we can find the numerical equivalent of 12^2 by multiplying 12 by itself:
12^2 = 12 * 12 = 144.
Therefore, the numerical equivalent of 12^-5 * 12^7 is 144.