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Find the cube roots of the following:

(a) [tex]\(-4,913 \times 512\)[/tex]

(b) [tex]\(729 \times 4,096\)[/tex]

(c) [tex]\(-\frac{27}{125}\)[/tex]

(d) [tex]\(0.000036\)[/tex]

Answer :

Let's find the cube roots for each given expression.

### (a) [tex]\(-4,913 \times 512\)[/tex]

Step 1: Compute the product [tex]\(-4,913 \times 512\)[/tex].
[tex]\[
-4,913 \times 512 = -2,514,816
\][/tex]

Step 2: Find the cube root of [tex]\(-2,514,816\)[/tex].
[tex]\[
\sqrt[3]{-2,514,816} = -136.0
\][/tex]

Thus, the cube root of [tex]\(-4,913 \times 512\)[/tex] is [tex]\(-136.0\)[/tex].

### (b) [tex]\(729 \times 4,096\)[/tex]

Step 1: Compute the product [tex]\(729 \times 4,096\)[/tex].
[tex]\[
729 \times 4,096 = 2,986,944
\][/tex]

Step 2: Find the cube root of [tex]\(2,986,944\)[/tex].
[tex]\[
\sqrt[3]{2,986,944} = 144.0
\][/tex]

Thus, the cube root of [tex]\(729 \times 4,096\)[/tex] is [tex]\(144.0\)[/tex].

### (d) [tex]\(-\frac{27}{125}\)[/tex]

Step 1: Compute the value [tex]\(-\frac{27}{125}\)[/tex].
[tex]\[
-\frac{27}{125} = -0.216
\][/tex]

Step 2: Find the cube root of [tex]\(-0.216\)[/tex].
[tex]\[
\sqrt[3]{-0.216} = -0.6
\][/tex]

Thus, the cube root of [tex]\(-\frac{27}{125}\)[/tex] is [tex]\(-0.6\)[/tex].

### (e) [tex]\(0.000036\)[/tex]

Step 1: The given number is [tex]\(0.000036\)[/tex].

Step 2: Find the cube root of [tex]\(0.000036\)[/tex].
[tex]\[
\sqrt[3]{0.000036} = 0.03301927248894627
\][/tex]

Thus, the cube root of [tex]\(0.000036\)[/tex] is [tex]\(0.03301927248894627\)[/tex].

In summary:
- The cube root of [tex]\( -4,913 \times 512 \)[/tex] is [tex]\( -136.0 \)[/tex].
- The cube root of [tex]\( 729 \times 4,096 \)[/tex] is [tex]\( 144.0 \)[/tex].
- The cube root of [tex]\( -\frac{27}{125} \)[/tex] is [tex]\( -0.6 \)[/tex].
- The cube root of [tex]\( 0.000036 \)[/tex] is [tex]\( 0.03301927248894627 \)[/tex].

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