Determine if these numbers are rational or irrational
-3/13
Square root of 6
35
Square root of 4
7
0.12 repeated
Pi
-3/13: Rational (a fraction)
Square root of 6: Irrational (cannot be expressed as a fraction)
35: Rational (a whole number)
Square root of 4: Rational (equals 2, a whole number)
7: Rational (a whole number)
0.12 repeated: Rational (can be expressed as a fraction, 0.12 = 12/100)
Pi: Irrational (cannot be expressed as a fraction)
6^-6×6^?=6^11
To solve this equation, we need to use the exponent rule for multiplication. According to this rule, if we have the same base number raised to two different exponents, when multiplying them, we can add the exponents.
Given that 6^-6 * 6^? = 6^11, we can set up an equation as follows:
6^-6 * 6^? = 6^11
Since the base is the same, we can add the exponents:
6^(-6 + ?) = 6^11
Now, since the bases are the same and the powers are equal, we can equate the exponents:
-6 + ? = 11
To find the value of ?, we can solve the equation:
? = 11 - 6
? = 5
Therefore, 6^-6 * 6^5 = 6^11.
What's the missing value
The missing value in the equation "6^-6 * 6^?=6^11" is "?".
Based on the equation provided, we can solve for "?" by using the exponent rule for multiplication. According to this rule, when multiplying two numbers with the same base, the exponents can be added.
We start with:
6^-6 * 6^? = 6^11
Since the base is the same (6), we can add the exponents on the left side of the equation:
6^(-6 + ?) = 6^11
This equation tells us that the value of the exponent on the left side of the equation should be equal to 11. Therefore, we can state that:
-6 + ? = 11
To find the missing value "?", we can isolate it by adding 6 to both sides of the equation:
? = 11 + 6
? = 17
Therefore, the missing value in the equation is "?" = 17.
Simplify 5^-2×5^11
To simplify the expression 5^-2 * 5^11, we can use the exponent rule for multiplication, which states that when multiplying two numbers with the same base, the exponents can be added.
Here, we have the base 5 and two exponents: -2 and 11. To simplify, we add the exponents:
5^-2 * 5^11 = 5^(-2 + 11) = 5^9
Therefore, the simplified form of the expression 5^-2 * 5^11 is 5^9.