Question

1 7²+17^-5 = 17^-3 = 1/17³​

Answer 1

Step-by-step explanation:

[17

3

×17

2

5

×17

2

9

]×[17

7

10

×(17

5

)

5

3

×(17

6

)

7

1

]

−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}[17

3

×17

2

5

×17

2

9

]×[17

7

10

×17

3

×(17

7

6

]

−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

3+

2

5

+

2

9

]×[17

7

10

+3+

7

6

]

−1

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

10

]×[17

7

30

]

−1

Apply algebraic identify a⁻¹ = 1/a:

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

10

]÷[17

7

30

]

Apply algebraic identify aⁿ ÷ aˣ = aⁿ⁻ˣ:

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

17^\frac{33}{7}17

7

33