Answer :
Sure! Let's simplify the expression [tex]\(\sqrt[3]{5x} \cdot \sqrt[3]{25x^2}\)[/tex] step by step.
1. Combine the cube roots: According to the property of exponents, [tex]\(\sqrt[3]{a} \cdot \sqrt[3]{b} = \sqrt[3]{a \cdot b}\)[/tex]. Therefore, we can combine the two cube roots into one:
[tex]\[
\sqrt[3]{5x} \cdot \sqrt[3]{25x^2} = \sqrt[3]{(5x) \cdot (25x^2)}
\][/tex]
2. Multiply the terms inside the cube root: Now, multiply the terms inside:
[tex]\[
5x \cdot 25x^2 = (5 \cdot 25) \cdot (x \cdot x^2) = 125x^3
\][/tex]
3. Take the cube root of the product: Next, calculate the cube root of the product:
[tex]\[
\sqrt[3]{125x^3}
\][/tex]
- The cube root of 125 is 5 because [tex]\(5^3 = 125\)[/tex].
- The cube root of [tex]\(x^3\)[/tex] is x because [tex]\((x)^3 = x^3\)[/tex].
4. Result: Combine these results:
[tex]\[
\sqrt[3]{125x^3} = 5x
\][/tex]
Therefore, the simplified expression is [tex]\(5x\)[/tex].
The correct answer is [tex]\(5x\)[/tex].
1. Combine the cube roots: According to the property of exponents, [tex]\(\sqrt[3]{a} \cdot \sqrt[3]{b} = \sqrt[3]{a \cdot b}\)[/tex]. Therefore, we can combine the two cube roots into one:
[tex]\[
\sqrt[3]{5x} \cdot \sqrt[3]{25x^2} = \sqrt[3]{(5x) \cdot (25x^2)}
\][/tex]
2. Multiply the terms inside the cube root: Now, multiply the terms inside:
[tex]\[
5x \cdot 25x^2 = (5 \cdot 25) \cdot (x \cdot x^2) = 125x^3
\][/tex]
3. Take the cube root of the product: Next, calculate the cube root of the product:
[tex]\[
\sqrt[3]{125x^3}
\][/tex]
- The cube root of 125 is 5 because [tex]\(5^3 = 125\)[/tex].
- The cube root of [tex]\(x^3\)[/tex] is x because [tex]\((x)^3 = x^3\)[/tex].
4. Result: Combine these results:
[tex]\[
\sqrt[3]{125x^3} = 5x
\][/tex]
Therefore, the simplified expression is [tex]\(5x\)[/tex].
The correct answer is [tex]\(5x\)[/tex].
