What is the missing exponent in the following equation? h ^450/h^? = h^215
The missing exponent can be determined by subtracting the exponent of h on the left side of the equation from the exponent of h on the right side of the equation.
450 - ? = 215
To find the value of ?, we can rearrange the equation:
450 - 215 = ?
The result is:
? = 235
Therefore, the missing exponent is 235.
Simplify 12^87 divided by 12^25.
To simplify this expression, we use the rule of exponents that states "when dividing two powers with the same base, subtract the exponents." In this case, since we are dividing 12^87 by 12^25, we subtract the exponent of the denominator from the exponent of the numerator:
12^87 / 12^25
= 12^(87-25)
= 12^62
What is the missing number in this simplified exponential expression: 7^? Divided by 7^5 = 7^12?
To find the missing number in this simplified exponential expression, we apply the rule of exponents that states "when dividing two powers with the same base, subtract the exponents." In this case, since we are dividing 7^? by 7^5, we subtract the exponent of the denominator (5) from the exponent of the numerator (?):
7^? / 7^5 = 7^12
Using the rule mentioned, we can rewrite the equation:
7^(?-5) = 7^12
To make both sides of the equation equal, the exponents must be equal as well. Therefore, the missing number must be equal to:
? - 5 = 12
Adding 5 on both sides of the equation:
? = 12 + 5
? = 17
Thus, the missing number in the simplified exponential expression is 17.
What is the value of 6.9 - 2^0?
The value of 2^0 is 1, since any number raised to the power of 0 equals 1.
Therefore, 6.9 - 2^0 is equal to:
6.9 - 1 = 5.9
Apply the Zero Power rule to create an equivalent expression to 9• (-33)^0 + 3/2(8-27^0)?
According to the Zero Power rule, any non-zero number raised to the power of 0 equals 1.
Using this rule, we can simplify the expression 9• (-33)^0 to:
9 • 1
Which equals:
9
Additionally, 27^0 is also equal to 1, because any non-zero number raised to the power of 0 is 1.
Therefore, we can simplify 3/2(8-27^0) to:
3/2(8-1)
= 3/2(7)
= 3 * 7/2
= 21/2
Finally, the equivalent expression using the Zero Power rule is:
9 + 21/2
Solve the expression 15•8^0/5 + 4(7^0-6)?
To solve the expression 15•8^0/5 + 4(7^0-6), we need to follow the order of operations (PEMDAS/BODMAS).
First, let's simplify the exponent 8^0:
Any number raised to the power of 0 is equal to 1, so 8^0 = 1.
Now, we can solve the expression step by step:
15 • 1 / 5 + 4(1 - 6)
15 / 5 + 4(-5)
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?
To simplify (10^3)^6 using the Power Rule of Exponents, we multiply the exponents.
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?
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 * 7.
Use the Power Rule of Exponents to create a simplified equivalent expression for (19^4)^9?
To simplify (19^4)^9 using the Power Rule of Exponents, we multiply the exponents:
(19^4)^9 = 19^(4*9)
This simplifies to:
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 of decimals.
To solve 7^-3 using the property of negative integer exponents, we can apply the rule which states that any number raised to a negative exponent is equal to 1 divided by that number raised to the positive exponent.
Therefore, 7^-3 can be rewritten as:
1 / 7^3
Since 7^3 is equal to 7 * 7 * 7, we have:
1 / (7 * 7 * 7)
Simplifying further:
1 / 343
So, the value of 7^-3 is 1/343.
Apply the Property of Negative Integer Exponent 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 apply the property of negative integer exponents which states that any number raised to a negative exponent is equal to 1 divided by that number raised to the positive exponent.
Using this property, we can rewrite the expression as:
1 / (3^17) / (1 / 8^14)
Simplifying further, we can also apply the property of dividing powers with the same base by subtracting the exponents:
1 / (3^17) / (8^(-14))
Now, to eliminate the negative exponent in the denominator, we can apply the property of negative exponents which states that any number raised to a negative exponent is equal to its reciprocal raised to the positive exponent:
1 / (3^17) / (1 / (1 / 8^14))
Simplifying further:
1 / (3^17) / (1 / (8^14)^(-1))
1 / (3^17) / ((1 / 8^14)^1)
Finally, using the property of raising a power to a power:
1 / (3^17) / (8^(14 * 1))
The simplified expression with positive exponents only is:
1 / (3^17) / 8^14
Apply the Properties of integer Exponents to generate equivalent expressions to (7^-3)^7 • 7^20 with only positive exponents, then solve the expression. Provide the answer as an improper fraction?
To generate equivalent expressions for (7^-3)^7 • 7^20 with only positive exponents, we can apply the property of exponents which states that when raising a power to another power, we multiply the exponents:
(7^-3)^7 • 7^20
Using the property, we get:
7^(-3 * 7) • 7^20
Simplifying the exponents:
7^-21 • 7^20
Now, let's apply another property that when multiplying powers with the same base, we add the exponents:
7^(-21 + 20)
Further simplifying:
7^(-1)
To eliminate the negative exponent, we apply the property that a number raised to the power -1 is equal to its reciprocal:
1 / 7^1
Therefore, the expression (7^-3)^7 • 7^20 is equivalent to:
1 / 7
So, the answer is 1/7 expressed as an improper fraction.
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 an equivalent expression for (7^-3)^7 • 7^20/ 6^-2 with only positive exponents, we can apply the properties of exponents.
Starting with (7^-3)^7, we apply the property that when raising a power to another power, we multiply the exponents:
(7^-3)^7 = 7^(-3 * 7) = 7^-21
Next, we can simplify the expression by applying the property that a negative exponent can be rewritten as its reciprocal with a positive exponent:
7^-21 = 1/7^21
Now, let's focus on 7^20/6^-2. We can simplify this expression by applying the property of dividing powers with the same base, which states that we subtract the exponents:
7^20/6^-2 = 7^20 * 6^2
Now, we have the expression 1/7^21 * 7^20 * 6^2. To further simplify this, we can apply the property of multiplying powers with the same base, which states that we add the exponents:
1/7^21 * 7^20 * 6^2 = 1/7^(21-20) * 6^2 = 1/7^1 * 6^2 = 1/7 * 6^2 = 6^2/7
Therefore, the simplified expression is 6^2/7.
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?
To find the numerical equivalent of 12^-5 • 12^7 using the product rule of integer exponents, we can combine the two terms with the same base (12) by adding their exponents:
12^-5 • 12^7 = 12^(-5 + 7)
Now, we simplify the exponents:
12^(-5 + 7) = 12^2
Therefore, the numerical equivalent of 12^-5 • 12^7 is 12^2.