simplification of the expression 9 over h to the power of negative 3
One way to simplify the expression 9/h^(-3) is to use the rule of negative exponents, which states that any non-zero number raised to a negative exponent is equal to the reciprocal of the same number raised to the opposite, positive exponent. In other words:
a^(-n) = 1/a^n (when a ≠ 0)
Using this rule, we can rewrite h^(-3) as 1/h^3, and then simplify the original expression as:
9/h^(-3) = 9/(1/h^3) = 9 * h^3 = 9h^3
Therefore, 9/h^(-3) is equivalent to 9h^3.
To simplify the expression (9/h)^-3, first, we can invert the fraction inside the parentheses and change the sign of the negative exponent:
(9/h)^-3 = (h/9)^3
Next, we cube both the numerator and denominator to remove the exponent:
(h/9)^3 = (h^3) / (9^3)
Simplifying further, we can evaluate the denominator, 9^3, which is equal to 729:
(h^3) / (9^3) = (h^3) / 729
Therefore, the simplification of the expression (9/h)^-3 is (h^3) / 729.