Question

Simplify and express the result with positive exponent
(3) ^ 5 * (5/3) ^ 7​

Answer 1

Answer:

5⁷/3²

Step-by-step explanation:

3⁵*(5/3)⁷

= 3⁵*(5⁷/3⁷)

= 3⁵*5⁷*3⁻⁷

= 5⁷*3⁻⁷⁺⁵

= 5⁷*3⁻²

= 5⁷/3²

Answer 2

Question:

Simplify and express the result with positive exponent   $3^5\times(\frac{5}{3})^7$

Solution:

$3^5\times(\frac{5}{3})^7\\\\\\(\frac{a}{b})^m=\frac{a^m}{b^m}\\\\\\3^5\times\frac{5^7}{3^7}\\\\\\a^m\times\frac{b^n}{a^n}=\frac{b^n}{a^{n-m}}\\\\\\\frac{5^7}{3^{7-5}}\\\\\\\frac{5^7}{3^2}\\\\\\\boxed{=\frac{5^7}{3^2}}$

Answer:

The product of  $3^5\times(\frac{5}{3})^7$ is  $\frac{5^7}{3^2}$

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