(5-¹x 7²/
5² x 7-⁴)⁷/²
Answers
answer:
Step-by-step explanation:
(i) (16⁻¹/⁵)⁵/²
= (16)⁻¹/⁵× ⁵/²
[(am)n = amn]
= (16)⁻¹/²
= (4²)⁻¹/²
= 4²×⁻¹/²
= 4⁻¹
[a⁻¹ = 1/a]
= 1/4
(ii) ³√(343)⁻²
= (343)⁻²/³
= (7³)⁻²/³
= 7⁻²
= (1/7)²
= 1/49
(iii) (0.001)¹/³
= (1/10³)¹/³
= (1/10³×¹/³)
= 1/10
= 0.1
(iv) (25)³/² x (243)³/⁵ / (16)⁵/⁴ x (8)⁴/³
= [(5²)³/² × 3⁵׳/⁵] / [(2⁴)⁵/⁴ × 2³×⁴/³]
= [5³ × 3³]/ [2⁵ × 2⁴]
= [125 × 27]/ [32 × 16]
= 3375/512
(v) (√2/5)⁸ ÷(√2/5)¹³
= (√2/5)⁸ ⁻¹³
= (√2/5)⁻⁵
= (5/√2)⁵
[a^-p = 1/ a^p]
= 3125/4√2
(vi) (5⁻¹x 7²/ 5² x 7⁻⁴)⁷/² x (5⁻² x 7³/ 5³ x 7⁻⁵)⁻⁵/²
= [(5⁻¹×⁷/² x 7²×⁷/² / [5²×⁷/² x 7⁻⁴×⁷/² )] x [(5⁻²×⁻⁵/² x 7³×⁻⁵/² / 5³×⁻⁵/² x 7⁻⁵ ×⁻⁵/²)]
= [5⁻⁷/² × 7⁷/ 5⁷ × 7⁻¹⁴] / [5⁵ × 7⁻¹⁵/² / 5⁻¹⁵/² × 7²⁵/²]
= [5⁻⁷/² ⁻ ⁷ × 7⁷⁺¹⁴] / [5⁵ ⁺ ¹⁵/² × 7⁻¹⁵/² ⁺ ²⁵/²]
= [5(⁻ ⁷⁻¹⁴)/² × 7²¹] / [5²⁵/² × 7⁻⁴⁰/²
= [5(⁻²¹/²⁵)/² × 7²¹] / [5²⁵/² × 7⁻⁴⁰/²
= 5(⁻²¹⁺²⁵)/² × 7²¹⁻ ²⁰
= 5⁴/² × 7¹
= 5² × 7
= 25 × 7
= 175
Step-by-step explanation:
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