Question

(q^4)=q^12
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Answer 1

In order for (
`q^4`) to equal
`q^(12)`, it implies that q must be raised to the power of 3. Therefore, q = 1 is the solution, as
`(1^4) = 1^(12) = 1.`

The given equation
`\( (q^4) = q^(12) \)` indicates an equality involving powers of q. To determine the value of q, we observe that
`\( q^(12) \)` can be expressed as
`\( (q^4)^3 \)` due to the exponent property that when a power is raised to another power, the exponents multiply.

Consequently,
`\( (q^4) = q^(12) \)` simplifies to
`\( q^3 = 1 \)`. The solution is q = 1 since any non-zero number raised to the power of 3 equals 1. This outcome aligns with the original equation, validating the solution.

Thus, the value of q that satisfies
`\( (q^4) = q^(12) \)` is q = 1. The understanding of exponent properties and algebraic manipulation is crucial in solving such equations and arriving at a precise solution.

The probable question may be:

If \( (q^4) = q^{12} \), what is the value of \( q \)?