Question

What is the value of (343) -1/3

Answer 1

$(343)^{\frac{-1}{3} }$ = 1/7

Given:

$(343)^{\frac{-1}{3} }$

To Find:

Value

Solution:

• a³ = a × a × a
• ∛a³ = a
• (xᵃ)ᵇ = xᵃᵇ
• x⁻ᵃ = 1/xᵃ
• x¹ = x
• "Prime Factorization is finding prime numbers/factors which when multiplied together results in the original number"
• Prime number is a natural number which has only two factors one and number itself.  (e.g. , 2 , 3 , 5 , 7 .... )

Step 1:

Prime factorize 343

343 = 7 × 7 × 7

343 = 7³

Step 2:

Substitute 343 = 7³

$(7^3)^{\frac{-1}{3} }$

Step 3:

Use (xᵃ)ᵇ = xᵃᵇ

$7^{(3 \times{\frac{-1}{3})} \\= 7^{-1}$

Step 4:

Use x⁻ᵃ = 1/xᵃ  and x¹ = x

= 1/7¹

= 1/7

Hence $(343)^{\frac{-1}{3} }$ = 1/7