Find the value of: $1^3 + 5^3 + 7^3$
Find the value of: $5^3 – 7^3$
Find the value of: $10^3$
Find the value of: $(-4)^3 + (4)^3$
Write $6 \times 6 \times 6$ in cube form and find its value.
Find the cube of 15.
Find the values of:
a) $17^3$
b) $20^3$
If $x^3 = 729$, find the value of $x$.
If $x^3 = 512$, find the value of $x$.
Find the cube of 100.
Find the value of: $1^3 + 5^3 + 7^3$
First, calculate each cube: $1 \times 1 \times 1 = 1$; $5 \times 5 \times 5 = 125$; $7 \times 7 \times 7 = 343$.
Add them together: $1 + 125 + 343 = 469$.
Find the value of: $5^3 – 7^3$
Calculate the cubes: $5^3 = 125$ and $7^3 = 343$.
Subtract the larger number from the smaller one: $125 – 343 = -218$.
Find the value of: $10^3$
To cube 10, multiply it by itself three times: $10 \times 10 \times 10$.
A quick trick for powers of 10 is to write ‘1’ followed by the number of zeros indicated by the exponent: 1,000.
Find the value of: $(-4)^3 + (4)^3$
$(-4)^3$ results in a negative value because an odd number of negatives stay negative: $-4 \times -4 \times -4 = -64$.
$(4)^3$ is $4 \times 4 \times 4 = 64$.
Adding them gives: $-64 + 64 = 0$.
Write $6 \times 6 \times 6$ in cube form and find its value.
“Cube form” means using an exponent of 3: $6^3$.
Calculating the value: $6 \times 6 = 36$, and $36 \times 6 = 216$.
Find the cube of 15.
Multiply 15 by itself three times: $15 \times 15 = 225$.
Then, $225 \times 15 = 3,375$.
Find the values of: a) $17^3$ and b) $20^3$
a) $17 \times 17 \times 17 = 4,913$.
b) For $20^3$, you can cube the 2 ($2 \times 2 \times 2 = 8$) and then add three zeros: 8,000.
If $x^3 = 729$, find the value of $x$.
This is asking for the cube root of 729.
Since $9 \times 9 \times 9 = 729$, the value of $x$ is 9.
If $x^3 = 512$, find the value of $x$.
Find the number that, when multiplied by itself three times, equals 512.
Through estimation or factorization: $8 \times 8 \times 8 = 512$, so $x = 8$.
Find the cube of 100.
Multiply $100 \times 100 \times 100$.
Following the zero rule, you write ‘1’ and then six zeros (two zeros for each of the three factors): 1,000,000