Question

Simplify. Assume all variables represent nonzero real numbers. The final answer should not contain negative exponents. ((k¹⁴m⁹)/(3k⁻²m⁴))²

Answer 1

To simplify ((k¹⁴m⁹)/(3k⁻²m⁴))², distribute the negative exponent in the denominator, add the exponents of k, subtract the exponents of m, and apply the square to all terms, yielding k³²m¹⁰ / 9 as the final simplified expression without any negative exponents.

Step-by-step explanation:

The question involves simplifying an expression with exponents according to the algebraic rules of powers. First, we need to simplify the expression inside the parentheses by applying the exponent to both the numerator and denominator separately. To remove the negative exponent, we'll use the rule that a-n = 1/an. Then, the squared term outside the parentheses will be applied to every term inside.

Let's break it down step by step:

1. Simplify the expression inside the parentheses by applying the negative exponent in the denominator: ((k14m9)/(3k-2m4)).
2. Rewrite the negative exponent as k2 in the numerator, which gives us ((k14+2m9)/(3m4)).
3. Simplify the exponents for k and subtract the exponents for m: ((k16m9-4)/3).
4. Now we have ((k16m5)/3).
5. Finally, apply the squared term to every term inside the parentheses: (k162 * m52 / 32) = k32m10 / 9.

Therefore, the simplified expression without negative exponents is k32m10 / 9.