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Exercise

$\left(-3x^3y^4\right)^4$

Step-by-step Solution

1

The power of a product is equal to the product of it's factors raised to the same power

$\left(x^3\right)^4\left(-3y^4\right)^4$
2

Simplify $\left(x^3\right)^4$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $3$ and $n$ equals $4$

$x^{3\cdot 4}\left(-3y^4\right)^4$
3

Multiply $3$ times $4$

$x^{12}\left(-3y^4\right)^4$
4

Multiply $3$ times $4$

$x^{12}\left(-3y^4\right)^4$

Final answer to the exercise

$x^{12}\left(-3y^4\right)^4$

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Main Topic: Power of a product

The power of a product of factors is equal to the product of each factor to the same power: $\left(b\cdot c\right)^n=b^n\cdot c^n$.

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