Use a fractional exponent to write the expression the fourth root of 81 raised to the ninth power
what is 81^(9/4) ?
To write the expression "the fourth root of 81 raised to the ninth power" using a fractional exponent, we can break down the steps:
Step 1: Simplify the fourth root of 81:
The fourth root of 81 can be written as 81^(1/4).
Step 2: Raise the simplified expression to the ninth power:
To raise 81^(1/4) to the ninth power, we multiply the exponents. So, we get (81^(1/4))^9.
Step 3: Simplify the expression:
When we raise a power to another power, we multiply the exponents. So, we can rewrite the expression as 81^((1/4) * 9).
Step 4: Multiply the exponents:
(1/4) multiplied by 9 is equal to 9/4. Therefore, the final expression is 81^(9/4).
To write the expression "the fourth root of 81 raised to the ninth power" using fractional exponents, we need to first understand what it means.
"The fourth root of 81" refers to finding a number that, when raised to the fourth power, equals 81. In other words, we need to find a number, let's call it "x," where x^4 = 81.
To find this number, we take the fourth root of 81, which is denoted as 81^(1/4) or "81 raised to the one-fourth power."
Now, to raise this value to the ninth power, we multiply it by itself nine times. We can represent this as (81^(1/4))^9.
To simplify this expression, we multiply the exponents: 1/4 * 9 = 9/4.
Therefore, the expression "the fourth root of 81 raised to the ninth power" can be written as 81^(9/4).