Write as a monomial in standard form:(–0.6m^3n^2)^3
The answer is -0.216m^9n^6
The 9 N and the 6 are exponents
. − 0.216 m 9 n 6
1. (-0.6^1*3 * m^3*3 * n^2*3)
2. -0.6^3 * m^9 * n^6
3. -(0.6 * 0.6 * 0.6) = -0.216
therefore the answer is -0.216m^9n^6
^ this symbol means the number after it is an exponent
how?
Sure! Let's break it down step by step. First, we need to raise the monomial (-0.6m^3n^2) to the power of 3.
((-0.6m^3n^2)^3)
Now, let's expand it by applying the power rule. We multiply the exponents of each term inside the parentheses by 3.
=(-0.6)^3 * (m^3)^3 * (n^2)^3
=(-0.6)^3 * m^(3*3) * n^(2*3)
=(-0.216) * m^9 * n^6
So, the monomial in standard form is -0.216m^9n^6.
And remember, math jokes are always a plus!
To write the monomial (–0.6m^3n^2)^3 in standard form, we need to first expand the expression using the exponent rule for exponentiating a power. According to this rule, to raise a power to another power, you need to multiply the exponents.
So, applying this rule to our expression, we have:
(–0.6m^3n^2)^3 = –0.6^3 * (m^3)^3 * (n^2)^3
Simplifying further, we obtain:
= –0.6^3 * m^(3*3) * n^(2*3)
= –0.6^3 * m^9 * n^6
Now we can evaluate the value of –0.6^3, which is (-0.6) * (-0.6) * (-0.6) = 0.216.
Plugging this value back into the expression, we get:
= 0.216 * m^9 * n^6
Therefore, the monomial (–0.6m^3n^2)^3, written in standard form, is 0.216m^9n^6.