Answer :
To simplify the expression [tex]\(\sqrt[3]{5x} \cdot \sqrt[3]{25x^2}\)[/tex], we can use the property of cube roots: [tex]\(\sqrt[3]{a} \cdot \sqrt[3]{b} = \sqrt[3]{a \times b}\)[/tex]. This lets us combine the two cube roots into a single cube root:
1. Multiply the expressions inside the cube roots:
[tex]\[ 5x \times 25x^2 = 125x^3 \][/tex]
2. Now, take the cube root of the product:
[tex]\[ \sqrt[3]{125x^3} \][/tex]
3. Simplify the cube root:
- [tex]\(\sqrt[3]{125}\)[/tex] simplifies to 5 because [tex]\(5 \times 5 \times 5 = 125\)[/tex].
- [tex]\(\sqrt[3]{x^3}\)[/tex] simplifies to [tex]\(x\)[/tex] because the cube root and the exponent cancel each other out.
4. Combine these results:
[tex]\[ \sqrt[3]{125x^3} = 5x \][/tex]
So, the completely simplified expression is [tex]\(5x\)[/tex].
1. Multiply the expressions inside the cube roots:
[tex]\[ 5x \times 25x^2 = 125x^3 \][/tex]
2. Now, take the cube root of the product:
[tex]\[ \sqrt[3]{125x^3} \][/tex]
3. Simplify the cube root:
- [tex]\(\sqrt[3]{125}\)[/tex] simplifies to 5 because [tex]\(5 \times 5 \times 5 = 125\)[/tex].
- [tex]\(\sqrt[3]{x^3}\)[/tex] simplifies to [tex]\(x\)[/tex] because the cube root and the exponent cancel each other out.
4. Combine these results:
[tex]\[ \sqrt[3]{125x^3} = 5x \][/tex]
So, the completely simplified expression is [tex]\(5x\)[/tex].
