Find the numerical equivalent of 9^9⋅9^−6
To find the numerical equivalent of 9^9 * 9^-6, we can simplify each term separately.
First, we calculate 9^9 as follows:
9^9 = 387,420,489
Next, we calculate 9^-6:
9^-6 = 1/9^6 = 1/531,441
Now, we can multiply the two terms together:
387,420,489 * (1/531,441) = 387,420,489/531,441
Simplifying the fraction, we have:
387,420,489/531,441 = 729
Therefore, the numerical equivalent of 9^9 * 9^-6 is 729.
What is the missing exponent in the following equation?
h^450 / h^? = h^215
To find the missing exponent in the equation h^450 / h^? = h^215, we can apply the rules of exponentiation.
When dividing two numbers with the same base but different exponents, we subtract the exponents. Therefore, we can rewrite the equation as:
h^(450 - ?) = h^215
This equation shows that the exponent on both sides of the equation is equal. Thus, we can set the exponents equal to each other:
450 - ? = 215
Now we solve for the missing exponent, ?:
450 - 215 = ?
235 = ?
Therefore, the missing exponent is 235.
Simplify 12^87÷12^25
To simplify 12^87 ÷ 12^25, we can use the rule of exponentiation that states when dividing numbers with the same base, we subtract the exponents.
Using this rule, we can rewrite the expression as:
12^(87 - 25)
Now, we can subtract the exponents:
12^62
Therefore, 12^87 ÷ 12^25 simplifies to 12^62.
What is the missing number in this simplified exponential expression: 7^?÷7^5=7^12?
To find the missing number in the expression 7^? ÷ 7^5 = 7^12, we can apply the rule of exponentiation for dividing numbers with the same base.
The rule states that when dividing numbers with the same base, we subtract the exponents.
Using this rule, we can rewrite the expression as:
7^(? - 5) = 7^12
Since both sides of the equation have the same base, we can set the exponents equal to each other:
? - 5 = 12
Now, solve for the missing number:
? = 12 + 5
? = 17
Therefore, the missing number in the simplified exponential expression is 17.
What is the value of 6.9−2^0
The value of 6.9 - 2^0 can be calculated by evaluating the exponent first:
2^0 is equal to 1 (since any number raised to the power of 0 is 1).
Therefore, the expression simplifies to:
6.9 - 1
Subtracting 1 from 6.9 gives us the final value:
6.9 - 1 = 5.9
So, the value of 6.9 - 2^0 is 5.9.
Apply the Zero Power Rule to create an equivalent expression to 9⋅(−33)0+32(8−270).
Applying the Zero Power Rule, any non-zero number raised to the power of zero is equal to 1.
In the given expression, we have:
9 ⋅ (-33)^0 + 32(8 - 270)
Since (-33)^0 is equal to 1, the expression simplifies to:
9 ⋅ 1 + 32(8 - 270)
Now, we can simplify the remaining terms inside the parentheses:
9 + 32( -262)
Finally, we can perform the multiplication and addition:
9 + (-8,384)
The result is:
-8,375
Therefore, the equivalent expression using the Zero Power Rule is -8,375.
Solve the expression 15⋅8^0/5+4(7^0−6)
To solve the expression 15 ⋅ 8^0 / 5 + 4(7^0 - 6), we'll follow the order of operations (PEMDAS/BODMAS) which states we should perform any calculations inside parentheses/brackets first, then exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right.
First, we'll evaluate the exponents:
8^0 = 1
7^0 = 1
Now, let's simplify the expression:
15 ⋅ 8^0 / 5 + 4(7^0 - 6)
= 15 ⋅ 1 / 5 + 4(1 - 6)
= 15 / 5 + 4(-5)
= 3 + 4(-5)
= 3 + (-20)
= -17
Therefore, the solution to the expression 15 ⋅ 8^0 / 5 + 4(7^0 - 6) is -17.