Write the expression as a cube of a monomial.
– 8/27a^15
Sure, let's turn this expression into a cube of a monomial.
Since we're looking for a cube, we need to find the cube root of the expression. The cube root of -8/27a^15 is -2/3a^5.
So the expression - 8/27a^15 can be written as the cube of the monomial -2/3a^5. But don't worry, it's only a mathematical cube, not a literal one!
To write the expression as a cube of a monomial, we can rewrite it in the form (k * a^m)^3, where k is a constant and m is an exponent.
In this case, the expression is -8/27a^15.
Step 1: Simplify the coefficient
The coefficient is -8/27, which can be simplified. Both the numerator and denominator can be divided by 8.
-8/27 ÷ 8/8 = -1/3
Step 2: Rewrite the base
The base is a^15. We want to rewrite it as a power of a.
a^15 = (a^5)^3
Step 3: Rewrite the expression
Now, we can combine the simplified coefficient and the rewritten base to get the expression as a cube of a monomial.
(-1/3 * (a^5))^3 = (-(1/3)a^5)^3
Therefore, -8/27a^15 can be written as a cube of the monomial -(1/3)a^5.
To express the given expression –8/27a^15 as a cube of a monomial, we need to find a value that, when multiplied by itself three times, equals –8/27a^15.
First, let's rewrite the expression as –(2/3)^3a^15. This is because –8/27 is equal to –(2/3)^3, and a^15 can be considered as a monomial.
So, the expression –8/27a^15 can be written as –(2/3)^3a^15.
-8/27 = (-2/3)^3 and a^15 = (a^5)^3
so ....