Question

evaluate these question ​

Answer 1

Answer:

• 1/5

• 49/729

• 25/72

Step-by-step explanation:

$\sf \: (ii)(5 ^{ - 4} ) \times {5}^{ - 5}$

$\sf \implies \: \dfrac{ \dfrac{1}{625} }{ { {5}^{ - 8} } } ( {5}^{ - 5} )$

$\sf \implies \: \dfrac{ \dfrac{1}{625} }{ \dfrac{1}{390625} } ( {5}^{ - 5} )$

$\sf \implies \: 625( {5}^{ - 5} )$

$\sf \implies \: 625 \times \dfrac{1}{3125}$

$\implies \: \dfrac{1}{5} = {5}^{ - 1}$

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$\sf iii) \: \dfrac{ ({9}^{ - 5}) \times ( {7}^{2}) }{ {3}^{ - 4} }$

$\sf \implies \: \dfrac{ \dfrac{1}{59049} }{ {3}^{ - 4} } {(7}^{2})$

$\sf \implies \: \dfrac{ \dfrac{1}{59049} }{ {3}^{ - 4} } (49)$

$\sf \implies \: \dfrac{ \dfrac{49}{59049} }{ {3}^{ - 4} }$

$\sf \implies \: \frac{49}{729}$

------------------------------------

$\sf iv) \: (4 ^{ - 2} \times {3}^{ - 2} ) \times {5}^{2} \div {2}^{ - 1} \times (7 ^{ - 1} {)}^{0}$

$\sf \implies \: \dfrac{(4 ^{ - 2})( {3}^{ - 2})( {5}^{2}) }{ {2}^{ - 1} } {(7 - 1)}^{0}$

$\sf \implies \: \dfrac{ \dfrac{1}{16}( {3}^{ - 2} )( {5}^{2} ) }{ {2}^{ - 1} } {(7 - 1)}^{0}$

$\implies \dfrac{25}{72}$

What you need to know ?

Here laws of exponents are used :-

• When multiplying like bases, the bases remains same while exponents gets add up.

a² × a²= a⁴

• When dividing like bases, the bases remain same while exponents get subtracted.

a² ÷ a² = a

a.a.a = a³

• Any non - zero number raised to the power zero is one.

a^0 = 1

• raising a power to a power multiplies the powers together.

(a¹)² = a²

A fraction raised to a negative power is reciprocal of the original.