Math  /  Algebra

Question7) (2a23y3)3\left(\frac{-2 a^{2}}{3 y^{3}}\right)^{3}

Studdy Solution

STEP 1

1. We are given an expression involving a fraction raised to a power.
2. The expression can be simplified by applying the power to both the numerator and the denominator separately.
3. The power applies to each factor inside the parentheses.

STEP 2

1. Apply the power to the numerator.
2. Apply the power to the denominator.
3. Simplify the resulting expression.

STEP 3

Apply the power of 3 to the numerator 2a2-2a^2:
(2a2)3=(2)3×(a2)3(-2a^2)^3 = (-2)^3 \times (a^2)^3
Calculate each part:
(2)3=8and(a2)3=a2×3=a6(-2)^3 = -8 \quad \text{and} \quad (a^2)^3 = a^{2 \times 3} = a^6
So, the numerator becomes:
8a6-8a^6

STEP 4

Apply the power of 3 to the denominator 3y33y^3:
(3y3)3=33×(y3)3(3y^3)^3 = 3^3 \times (y^3)^3
Calculate each part:
33=27and(y3)3=y3×3=y93^3 = 27 \quad \text{and} \quad (y^3)^3 = y^{3 \times 3} = y^9
So, the denominator becomes:
27y927y^9

STEP 5

Combine the simplified numerator and denominator to form the final expression:
8a627y9\frac{-8a^6}{27y^9}
This is the simplified form of the original expression.

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