Question

Simplify using the laws of exponents

Answer 1

Answer:

A) [(-3/2)^2]^-3 ÷ (-3/2)^3

= (-3/2)^6÷ (-3/2)^3

= (-3/2)^6-3

= (-3/2)^3

= -27/8

B) (3^-1 × 4^-1)^-2 +5^0

= (1/3 × 1/4)^-2 + 1

= (1/12)^-2 +1

= (12)^2+ 1

= (24)+1

= 25

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Step-by-step explanation:

Answer 2

Answer:

1) [(-3/2)^2]^-3 ÷ (-3/2)^3

{a^-n = 1/a^n}

= [(-3/2)^2]^3 ÷ (-3/2)^3

{(a^m)^n = a^mn}

= (-3/2^2×3) ÷ (-3/2)^3

= (-3/2^6) ÷ (-3/2)^3

{(a+b)^m ÷ (a+b)^n = (a+b)^m-n}

= -3/2^6-3

= -3/2^3

2) (3^-1×4^-1)^-2 + 5^0

{a^m × b^m = (a×b)^m} & {a^0 = 1}

= [(3×4)^-1]^-2 + 1

= (12^-1)^-2 + 1

{a^-n = 1/a^n}

= 1/(1/12^1)^2 + 1

= 1/(1/24) + 1

=1.0416666667