Simplify 11 to the negative 4th power over 11 to the 8th power.
1 over 11 to the 12th power
1 over 11 to the 4th power
11^4
11^12
To simplify 11 to the negative 4th power over 11 to the 8th power, we can use the rule that states when you divide two numbers with the same base, you subtract the exponents. So, 11 to the negative 4th power over 11 to the 8th power is equal to 11 to the negative 4th power minus 8th power. That can be written as 11^(-4-8), which simplifies to 11^(-12).
To simplify 1 over 11 to the 12th power, we know that any number raised to the power of 0 is equal to 1. Therefore, 11 to the 0 power is equal to 1. So, 1 over 11 to the 12th power is equal to 1 divided by 1, which simplifies to 1.
To simplify 1 over 11 to the 4th power, we know that any number raised to the power of 1 is equal to itself. Therefore, 11 to the 1st power is equal to 11. So, 1 over 11 to the 4th power is equal to 1 divided by 11, which cannot be simplified further.
To simplify 11^4, we multiply 11 four times. So, 11^4 is equal to 11 × 11 × 11 × 11, which simplifies to 14,641.
To simplify 11^12, we multiply 11 twelve times. So, 11^12 is equal to 11 × 11 × 11 × 11 × 11 × 11 × 11 × 11 × 11 × 11 × 11 × 11, which would be a very long calculation. The result is 313,842,837,672,1.
To simplify 11 to the negative 4th power over 11 to the 8th power, we can subtract the exponents:
11^(-4)/11^(8) = 11^(-4 - 8)
Simplifying further:
11^(-4 - 8) = 11^(-12)
Therefore, 11 to the negative 4th power over 11 to the 8th power simplifies to 11 to the negative 12th power.
To simplify 1 over 11 to the 12th power, we can rewrite it as a negative exponent:
1/(11^12) = 11^(-12)
Therefore, 1 over 11 to the 12th power simplifies to 11 to the negative 12th power.
Similarly, to simplify 1 over 11 to the 4th power, we can rewrite it as a negative exponent:
1/(11^4) = 11^(-4)
Therefore, 1 over 11 to the 4th power simplifies to 11 to the negative 4th power.
Now, to find the value of 11 raised to the 4th power, we multiply 11 by itself four times:
11^4 = 11 * 11 * 11 * 11 = 14,641
Therefore, 11 to the 4th power is equal to 14,641.
Finally, to find the value of 11 raised to the 12th power, we multiply 11 by itself twelve times:
11^12 = 11 * 11 * 11 * 11 * 11 * 11 * 11 * 11 * 11 * 11 * 11 * 11
Calculating this value is quite large and requires advanced computation.
To simplify the expression 11 to the negative 4th power over 11 to the 8th power, we can use the rule of exponents which states that for any non-zero number a, a to the power of -n is equal to 1 divided by a to the power of n.
So, 11 to the negative 4th power can be written as 1 divided by 11 to the 4th power. Similarly, 11 to the 8th power can be written as 11 to the power of 8.
Now, when we divide (or in this case, simplify) a fraction with the same base, we subtract the exponents. In this case, we subtract the exponent of the denominator from the exponent of the numerator.
Therefore, 11 to the negative 4th power over 11 to the 8th power simplifies to 1 over 11 to the power of (4 - 8), which is 1 over 11 to the negative 4th power.
Since any non-zero number to the power of 0 is equal to 1, we can rewrite 1 over 11 to the negative 4th power as 11 to the 0th power over 11 to the 4th power.
Using the same base division rule, we subtract the exponents and simplify further:
11 to the 0th power over 11 to the 4th power becomes 1 over 11 to the 4th power, which is the final simplified form of the expression.
Therefore, the simplified form is 1 over 11 to the 4th power.