How to Simplify Algebraic Expressions Using Indices

What is the equivalent expression for (2a^-3b^4)^2 / (3a^5b)^-2)^-1?

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Answer:

The expression that is equivalent to [(2a⁻³b⁴)²/(3a⁵b)⁻²]⁻¹ is; 1/(36a⁴b¹⁰)

The given expression is [(2a⁻³b⁴)²/(3a⁵b)⁻²]⁻¹. By simplifying the terms and applying the laws of indices, we can find that the equivalent expression is 1/(36a⁴b¹⁰).

Explanation:

Firstly, we rewrite the equation as [(2a⁻³b⁴)² × (3a⁵b)²]⁻¹.

We simplify (2a⁻³b⁴)² to get 4b⁸/a⁶, and (3a⁵b)² to get 9a¹⁰b².

After simplification, we have [(4b⁸/a⁶) × 9a¹⁰b²]⁻¹.

Using the laws of indices, we simplify a¹⁰/a⁶ to get a⁴, and b⁸ × b² to get b¹⁰.

Finally, [(4b⁸/a⁶) × 9a¹⁰b²]⁻¹ simplifies to (36a⁴b¹⁰)⁻¹, which equals 1/(36a⁴b¹⁰).

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