72L12 15L13 I am having hard time finding L 144 Can you ple

72=L^(1/2) (1.5L)^(1/3) I am having hard time finding L = 144 Can you please show me the steps?

Write it in exponent form,

72= (L)^1/2 (1.5L)^1/3

= (L)^1/2 (L)^1/3 (1.5)^1/3

⁼ (L)^5/6 (3/2)^1/3 . Addition rule of exponents, when base is same exponents add on multiplication.

Now raise both sides to the power 6,

(72)⁶= [(L)^5/6 (3/2)^1/3]⁶ Apply power rule of exponents

(72)⁶= (L)⁵ (3/2)²= L⁵ (9/4) ,

Hence

L⁵= (72)⁶ (4/9)

= (72)⁵ (72)(4/9) = (72)⁵ (32)= (72)⁵ (2)⁵= (144)⁵ (addition rule of exponents)

Hence L =144

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