Find the cube root of -343: ^3√-343
The cube root of -343 is -7, since -7 cubed equals -343.
To find the cube root of -343, we need to find a number that, when cubed, gives us -343.
One way to find the cube root is by using the exponentiation notation. The cube root of -343 can be written as ^3√-343.
Now, let's find the cube root of -343.
We can convert -343 into its prime factorization to make the calculation easier.
The prime factorization of -343 is -1 * 7 * 7 * 7.
We can see that there is one negative sign and three 7's.
To find the cube root, we need to take one 7 out from the three 7's since we are looking for a single factor when cubed.
So, the cube root of -343 is -7.
Therefore, the cube root of -343 is -7 (^3√-343 = -7).
To find the cube root of -343, we need to find a number that, when raised to the power of 3, equals -343.
Let's start by looking at the factors of 343. We can see that 7 × 7 × 7 = 343. Therefore, we can write -343 as -(7 × 7 × 7).
Applying the properties of exponents, we can rewrite this as -(7^3).
Now, we need to find the cube root of -343, which can be written as ^3√(-343).
The cube root of -343 is -7, because if we raise -7 to the power of 3 (or cube it), we get -7 × -7 × -7 = -343.
Therefore, the cube root of -343 is -7.