Question

Use the equation below to answer the question.

(−3)=27=1 Which equation could also be used to solve for x?
a.−27×3=x
b.−27−3=x
c.−1=(27÷3)=x
d.−1=(27×3)=x

Answer 1

The correct equation that represents the same solution for x as the equation (-3)^3 = 27 is option c: -1 = (27 ÷ 3) = x, as this represents the cube root of -27.

Step-by-step explanation:

The equation (-3)^3 = 27 is being solved for x. We need to find an equivalent equation that could be used to solve for x. To do this, we need to consider the operations involved in the equation and how we can represent them in an equivalent way.

Considering inversion or dividing, we know from the rules of exponents that a negative exponent represents the reciprocal of the base raised to the positive exponent. Therefore, (-3)^3 is the same as -1 times 3 raised to the power of 3. This means we are looking for an equation that appropriately represents taking the cube root of -27 and setting it equal to x.

Looking at the provided options, the correct equation that represents this operation is a. -27 × 3 = x because it incorrectly suggests multiplying -27 by 3 to find x. The correct representation for the cube root of -27 would be written as x = ∛(-27), which is equivalent to c. -1 = (27 ÷ 3) = x.