Question

simplify

(xy^3z^4)^4

Answer 1

solve x2 + 3 = 19

Answer 2

To simplify \((xy^3z^4)^4\), you can apply the power of a product rule, which states that \((a \cdot b)^n = a^n \cdot b^n\).

In this case, you can apply the exponent to each factor inside the parentheses:

\[
(xy^3z^4)^4 = x^4 \cdot (y^3)^4 \cdot (z^4)^4
\]

Next, simplify each term using the power of a power rule, which states that \((a^m)^n = a^{m \cdot n}\):

\[
(y^3)^4 = y^{3 \cdot 4} = y^{12}
\]
\[
(z^4)^4 = z^{4 \cdot 4} = z^{16}
\]

Now combine everything:

\[
x^4 \cdot y^{12} \cdot z^{16}
\]

Thus, the simplified expression is:

\[
\boxed{x^4 y^{12} z^{16}}
\]

Answer 3

To solve the equation \( x^2 + 3 = 19 \), follow these steps:

1. **Isolate \( x^2 \)** by subtracting 3 from both sides of the equation:

\[
x^2 = 19 - 3
\]

\[
x^2 = 16
\]

2. **Take the square root** of both sides to solve for \( x \):

\[
x = \pm \sqrt{16}
\]

\[
x = \pm 4
\]

So the solutions are:

\[
x = 4 \quad \text{and} \quad x = -4
\]

Thus, the final answer is:

\[
\boxed{4 \text{ and } -4}
\]