1 Answer

Bertone · Answer 1 · 2024-06-20T19:08:10+0000

Simplification of the expression using laws of exponents is: h(x) = 12(5)
.^(2x)

Laws of exponents?

Some of the laws of exponents are:

- When multiplying by like bases, keep the same bases and add exponents.

- When raising a base to a power of another, keep the same base and multiply by the exponent.

- If dividing by equal bases, keep the same base and subtract the denominator exponent from the numerator exponent.

The expression we want to solve is given as:

h(x) = 2 * 25
$.^{((x+3)/(2)) }$ * 6 * 125
$.^{((1)/(3)x - 1) }$

Using laws of exponents, this is simplified to get:

h(x) = 2 * 5²
$.^{((x+3)/(2)) }$ * 6 * 5³
$.^{((1)/(3)x - 1) }$

This simplifies to get:

h(x) = 12 * 5
.^((x + 3 + x - 3))

h(x) = 12(5)
.^(2x)

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