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QUESTION IMAGE

true or false ( 27^{\frac{4}{3}} = 81 ) ○ true ○ false

Question

true or false ( 27^{\frac{4}{3}} = 81 )
○ true
○ false

Explanation:

Step1: Rewrite base as power of 3

$27 = 3^3$

Step2: Simplify left-hand side

$27^{\frac{4}{3}} = (3^3)^{\frac{4}{3}} = 3^{3\times\frac{4}{3}} = 3^4$

Step3: Calculate $3^4$

$3^4 = 3\times3\times3\times3 = 81$

Step4: Compare both sides

Left-hand side equals right-hand side.

Answer:

True