Can some one explain why this can't work?

On one of the questions for the quizzes in Algebra Through Puzzles, I encountered this question.

Take a quick look at the solution and tell me why my solution is wrong.

$(\frac{1}{100})^2 \times (\frac{18}{5})^4 \times (\frac{5}{3})^8$

$(\frac{1}{100})^2 \times (\frac{18^2}{5^2})^2 \times (\frac{5^3}{3^3})^2$

$(\frac{18^2 \times 5^3}{10^2 \times 5^2 \times 3^3})^2$

$(\frac{9^2 \times 2^2 \times 5}{10^2 \times 3^3})^2$

$(\frac{3^4 \times 2^2 \times 5}{2^2 \times 5^2 \times 3^3})^2$

$(\frac{3}{5})^2$

$\frac{3^2}{5^2}$

$\frac{9}{25}$

$\boxed{\frac{9}{25}}$

#Algebra

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`2 \times 3`	$2 \times 3$
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Comments

The exponent of $2^3$ cannot be transferred to $\dfrac{5}{3}$ . They're different bases!

Isaac Lu - 3 years, 1 month ago

2nd STEP

(5/3)^8 = (5^4/3^4)^2

Eduardo AG_182 - 3 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$