Question

(–6⁴)⁴,Simplify it using laws of exponents.

Answer 1

Solution :

( -6⁴ )⁴

= ( -6 )^4×4

[Since ( a^m )^n = a^mn ]

= ( -6 )^16

= 6^16

••••

Answer 2

( - 6⁴ )⁴



From the laws of exponents, we know that ( a² ) ⁿ = a²ⁿ or $(a^{n} )^{m}=a^{nm}$


On the basis of the discussed law of the exponent, we get : -


→ ( - 6⁴ )⁴

→ ( - 6 ) ${}^{4 \times 4 }$

→ ( - 6 ) ${}^{16}$



From the laws of exponents, we know that any negative number having any even number in its power is directly equal to the same number with positive sign. Like : ( - a )ⁿ = aⁿ { where n is the positive even number }.


→ 6${}^{16}$



Therefore, ( - 6⁴ )⁴ = 6${}^{16}$