Simplify.
(16/81)^-3/2
I don’t quite understand what to do with this problem can someone please explain it to me so I understand it
rules of exponents
inverting the fraction changes the sign of the exponent
fractional exponent is a root ...x^1/2 = √x
(16/81)^-3/2 = (81/16)^3/2 = (√81 / √16)^3
To simplify the expression (16/81)^(-3/2), we need to apply the rules of exponents.
First, let's start by rewriting the expression in a different form, using the reciprocal property of exponents. According to this property, for any non-zero value x, x^(-a) is equal to 1/x^a. So, we can rewrite (16/81)^(-3/2) as 1 / (16/81)^(3/2).
Next, we need to simplify the expression inside the parentheses. The expression (16/81)^(3/2) means we need to raise 16/81 to the power of 3/2.
To do this, we can separately raise the numerator (16) and the denominator (81) to the power of 3/2.
16^(3/2) = (sqrt(16))^3 = 4^3 = 64
81^(3/2) = (sqrt(81))^3 = 9^3 = 729
Now, we substitute these values back into our expression:
1 / (16/81)^(3/2) = 1 / (64/729)
Since dividing by a fraction is the same as multiplying by its reciprocal, we can rewrite this as:
1 * (729/64) = 729/64
Therefore, the simplified form of (16/81)^(-3/2) is 729/64.