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