Question

(17^(3) * (17)^5/2 * (17)^(9/2)) * (17^(10/7) * (17^5)^(3/5) * (17^6)^(1/7))^-1

Answer 1

$[ 17^3 \times 17^ \frac{5}{2} \times 17^\frac{9}{2} ] \times [ 17^ \frac{10}{7} \times (17^5)^ \frac{3}{5} \times (17^6)^\frac{1}{7} ]^{-1}$

Apply algebraic identify (aⁿ)ˣ = aⁿˣ:

$[ 17^3 \times 17^ \frac{5}{2} \times 17^\frac{9}{2} ] \times [ 17^ \frac{10}{7} \times 17^3 \times (17^\frac{6}{7} ]^{-1}$

Apply algebraic identify aⁿ x aˣ = aⁿ⁺ˣ:

$[ 17^{3 + \frac{5}{2} +\frac{9}{2}} ] \times [ 17^ {\frac{10}{7} + 3 + \frac{6}{7}} ]^{-1}$

$[ 17^{10} ] \times [ 17^ {\frac{30}{7}}]^{-1}$

Apply algebraic identify a⁻¹ = 1/a:

$[ 17^{10} ] \div [ 17^ {\frac{30}{7}}]$

Apply algebraic identify aⁿ ÷ aˣ = aⁿ⁻ˣ:

$17^{10 - \frac{30}{7}$

$17^\frac{33}{7}$

Answer 2

17 .........


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