To solve for x, let's first simplify the equation:
5 - 5^2 * 5x = 5 * 12^2
5 - 25 * 5x = 5 * 144
5 - 125x = 720
Now, let's isolate the x term:
125x = 720 - 5
125x = 715
Finally, divide both sides of the equation by 125 to solve for x:
x = 715 / 125
x = 5.72
5 minus 5 squared times 5x =5 12 squared
X = squared number
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5-⁵×5x=5¹²
X = squared
Find x
X = squared
Find x
To solve for x, let's start by simplifying the equation:
5 - 5^(-5) * 5x = 5^12
5 - (1/5^5) * 5x = 5^12
Next, let's convert 5^(-5) to a fraction:
5^-5 = 1/5^5
Substituting this back into the equation:
5 - (1/5^5) * 5x = 5^12
5 - (1/(5^5)) * 5x = 5^12
Now, let's simplify further:
5 - (1/(3125)) * 5x = 5^12
To eliminate the fraction, we can multiply both sides of the equation by 3125:
5 * 3125 - 3125 * (1/(3125)) * 5x = 3125 * 5^12
15625 - 5x = 244140625
Next, let's isolate the x term:
-5x = 244140625 - 15625
-5x = 244124000
Finally, divide both sides of the equation by -5 to solve for x:
x = 244124000 / -5
x = -48824800
5 - 5^(-5) * 5x = 5^12
5 - (1/5^5) * 5x = 5^12
Next, let's convert 5^(-5) to a fraction:
5^-5 = 1/5^5
Substituting this back into the equation:
5 - (1/5^5) * 5x = 5^12
5 - (1/(5^5)) * 5x = 5^12
Now, let's simplify further:
5 - (1/(3125)) * 5x = 5^12
To eliminate the fraction, we can multiply both sides of the equation by 3125:
5 * 3125 - 3125 * (1/(3125)) * 5x = 3125 * 5^12
15625 - 5x = 244140625
Next, let's isolate the x term:
-5x = 244140625 - 15625
-5x = 244124000
Finally, divide both sides of the equation by -5 to solve for x:
x = 244124000 / -5
x = -48824800
Five × negative five squared × 5 and 2 squared
To simplify the expression, let's break it down step by step:
First, let's calculate (-5)^2, which means multiplying -5 by itself:
(-5)^2 = (-5) × (-5) = 25
So now we have:
5 × 25 × 5^2
Next, let's calculate 5^2, which means multiplying 5 by itself:
5^2 = 5 × 5 = 25
Now we have:
5 × 25 × 25
To simplify further, we can multiply the numbers:
5 × 25 × 25 = 625 × 5
Multiplying again, we get the final result:
625 × 5 = 3125
Therefore, the expression "Five × negative five squared × 5 and 2 squared" simplifies to 3125.
First, let's calculate (-5)^2, which means multiplying -5 by itself:
(-5)^2 = (-5) × (-5) = 25
So now we have:
5 × 25 × 5^2
Next, let's calculate 5^2, which means multiplying 5 by itself:
5^2 = 5 × 5 = 25
Now we have:
5 × 25 × 25
To simplify further, we can multiply the numbers:
5 × 25 × 25 = 625 × 5
Multiplying again, we get the final result:
625 × 5 = 3125
Therefore, the expression "Five × negative five squared × 5 and 2 squared" simplifies to 3125.
Five times negative five squared times 5 and 4 squared
To simplify the expression, let's break it down step by step:
First, let's calculate (-5)^2, which means multiplying -5 by itself:
(-5)^2 = (-5) × (-5) = 25
So now we have:
5 × 25 × 5^4
Next, let's calculate 5^4, which means multiplying 5 by itself four times:
5^4 = 5 × 5 × 5 × 5 = 625
Now we have:
5 × 25 × 625
To simplify further, we can multiply the numbers:
5 × 25 × 625 = 78125
Therefore, the expression "Five times negative five squared times 5 and 4 squared" simplifies to 78125.
First, let's calculate (-5)^2, which means multiplying -5 by itself:
(-5)^2 = (-5) × (-5) = 25
So now we have:
5 × 25 × 5^4
Next, let's calculate 5^4, which means multiplying 5 by itself four times:
5^4 = 5 × 5 × 5 × 5 = 625
Now we have:
5 × 25 × 625
To simplify further, we can multiply the numbers:
5 × 25 × 625 = 78125
Therefore, the expression "Five times negative five squared times 5 and 4 squared" simplifies to 78125.
Equations equaling 5¹²
To find equations that equal 5^12, we can solve for x in various mathematical expressions. Here are a few examples:
1. x = 5^12
This equation directly states that x is equal to 5^12.
2. x + 5^2 = 5^12
By subtracting 5^2 from both sides, we can solve for x:
x = 5^12 - 5^2 = 244140600
3. 5^(2x) = 5^12
Since the base is the same on both sides, the exponents must be equal:
2x = 12
Dividing both sides by 2, we find:
x = 6
4. log₅(5^12) = x
Using logarithmic properties, we know that log₅(5^12) is equal to the exponent:
x = 12
5. 5 * x^2 = 5^12
Dividing both sides by 5, we find:
x^2 = 5^10
Taking the square root of both sides and considering both positive and negative roots:
x = ±5^5 = ±3125
These are a few examples of equations that equal 5^12.
1. x = 5^12
This equation directly states that x is equal to 5^12.
2. x + 5^2 = 5^12
By subtracting 5^2 from both sides, we can solve for x:
x = 5^12 - 5^2 = 244140600
3. 5^(2x) = 5^12
Since the base is the same on both sides, the exponents must be equal:
2x = 12
Dividing both sides by 2, we find:
x = 6
4. log₅(5^12) = x
Using logarithmic properties, we know that log₅(5^12) is equal to the exponent:
x = 12
5. 5 * x^2 = 5^12
Dividing both sides by 5, we find:
x^2 = 5^10
Taking the square root of both sides and considering both positive and negative roots:
x = ±5^5 = ±3125
These are a few examples of equations that equal 5^12.
Five times negative five to the second power times five to the power of blank equals five to the power of twelve
Let's solve the equation step by step:
5 * (-5)^2 * 5^x = 5^12
First, let's simplify (-5)^2:
(-5)^2 = (-5) * (-5) = 25
Now the equation becomes:
5 * 25 * 5^x = 5^12
Next, let's simplify 5^x * 5^2:
5^x * 5^2 = 5^(x+2)
Now the equation becomes:
5 * 25 * 5^(x+2) = 5^12
We can rewrite 5 and 25 as powers of 5:
5^1 * 5^2 * 5^(x+2) = 5^12
Now we can combine the terms with the same base:
5^(1 + 2 + x + 2) = 5^12
5^(5 + x) = 5^12
Since the bases are the same, we can equate the exponents:
5 + x = 12
Subtracting 5 from both sides:
x = 12 - 5
x = 7
Therefore, the equation 5 * (-5)^2 * 5^x = 5^12 has a solution of x = 7.
5 * (-5)^2 * 5^x = 5^12
First, let's simplify (-5)^2:
(-5)^2 = (-5) * (-5) = 25
Now the equation becomes:
5 * 25 * 5^x = 5^12
Next, let's simplify 5^x * 5^2:
5^x * 5^2 = 5^(x+2)
Now the equation becomes:
5 * 25 * 5^(x+2) = 5^12
We can rewrite 5 and 25 as powers of 5:
5^1 * 5^2 * 5^(x+2) = 5^12
Now we can combine the terms with the same base:
5^(1 + 2 + x + 2) = 5^12
5^(5 + x) = 5^12
Since the bases are the same, we can equate the exponents:
5 + x = 12
Subtracting 5 from both sides:
x = 12 - 5
x = 7
Therefore, the equation 5 * (-5)^2 * 5^x = 5^12 has a solution of x = 7.
Find the missing value for z⁸\cdotz times the power of blank =z¹⁵
To find the missing value, let's set up the equation:
z^8 * z^x = z^15
Now, let's use the rule of exponents that states when multiplying the same base with different exponents, we add the exponents:
z^(8 + x) = z^15
To solve this equation, we can equate the exponents:
8 + x = 15
Subtracting 8 from both sides of the equation:
x = 15 - 8
x = 7
So, the missing value for z^8 * z^x = z^15 is x = 7.
z^8 * z^x = z^15
Now, let's use the rule of exponents that states when multiplying the same base with different exponents, we add the exponents:
z^(8 + x) = z^15
To solve this equation, we can equate the exponents:
8 + x = 15
Subtracting 8 from both sides of the equation:
x = 15 - 8
x = 7
So, the missing value for z^8 * z^x = z^15 is x = 7.
4^7×4^x=4^12
To solve the equation, we can use the rule of exponents that states when multiplying the same base with different exponents, we add the exponents.
We have the equation:
4^7 * 4^x = 4^12
Using the rule, we can combine the exponents on the left side of the equation:
4^(7 + x) = 4^12
Now we can equate the exponents:
7 + x = 12
Subtracting 7 from both sides of the equation:
x = 12 - 7
x = 5
Therefore, the missing value for 4^7 * 4^x = 4^12 is x = 5.
We have the equation:
4^7 * 4^x = 4^12
Using the rule, we can combine the exponents on the left side of the equation:
4^(7 + x) = 4^12
Now we can equate the exponents:
7 + x = 12
Subtracting 7 from both sides of the equation:
x = 12 - 7
x = 5
Therefore, the missing value for 4^7 * 4^x = 4^12 is x = 5.
9×^-3x9^9
When you have a negative exponent, it means you take the reciprocal of the base raised to the positive exponent.
Let's simplify the expression step by step:
9^(-3) * 9^9
Since 9^(-3) is the reciprocal of 9^3, we can rewrite it as 1/(9^3):
1/(9^3) * 9^9
Next, we can simplify the multiplication by combining the exponents with the same base:
1/(9^3) * 9^(3*3)
Now we have:
1/(9^3) * 9^9
Simplifying further:
1/(9^3) * 9^9 = 1/729 * 9^9
To multiply fractions, we multiply the numerators and denominators separately:
(1 * 9^9) / (729)
Now we can simplify:
9^9 / 729 = 9^9 / 3^6
Since both 9 and 3 can be expressed as powers of 3:
(3^2)^9 / 3^6
Using the power of a power rule (raising a power to another power), we can simplify:
3^(2*9) / 3^6
3^18 / 3^6
Applying the rule of subtracting exponents when we have division:
3^(18 - 6) = 3^12
Therefore, 9^(-3) * 9^9 simplifies to 3^12.
Let's simplify the expression step by step:
9^(-3) * 9^9
Since 9^(-3) is the reciprocal of 9^3, we can rewrite it as 1/(9^3):
1/(9^3) * 9^9
Next, we can simplify the multiplication by combining the exponents with the same base:
1/(9^3) * 9^(3*3)
Now we have:
1/(9^3) * 9^9
Simplifying further:
1/(9^3) * 9^9 = 1/729 * 9^9
To multiply fractions, we multiply the numerators and denominators separately:
(1 * 9^9) / (729)
Now we can simplify:
9^9 / 729 = 9^9 / 3^6
Since both 9 and 3 can be expressed as powers of 3:
(3^2)^9 / 3^6
Using the power of a power rule (raising a power to another power), we can simplify:
3^(2*9) / 3^6
3^18 / 3^6
Applying the rule of subtracting exponents when we have division:
3^(18 - 6) = 3^12
Therefore, 9^(-3) * 9^9 simplifies to 3^12.
9 × negative power of 3 × 9 to the power of 9
To simplify the expression, let's break it down step by step:
First, let's calculate 3 raised to the power of 9:
3^9 = 19683
Now we have:
9 × (-3) × 19683
Next, let's calculate the negative power of 3:
(-3) = -3
Now we have:
9 × (-3) × 19683
To simplify further, we can multiply the numbers:
9 × (-3) × 19683 = -177147
Therefore, the expression "9 × negative power of 3 × 9 to the power of 9" simplifies to -177147.
First, let's calculate 3 raised to the power of 9:
3^9 = 19683
Now we have:
9 × (-3) × 19683
Next, let's calculate the negative power of 3:
(-3) = -3
Now we have:
9 × (-3) × 19683
To simplify further, we can multiply the numbers:
9 × (-3) × 19683 = -177147
Therefore, the expression "9 × negative power of 3 × 9 to the power of 9" simplifies to -177147.
1 answer