Maths-

General

Easy

Question

# Simplify: [[1/4]^{4} × [1/4]^{4}] ×[[3/^{5}]^{12} ÷ [3/5]^{5}]

Hint:

### In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.

an = a × a × ... x a n times.

## The correct answer is: Simplifying the given expression, we get the answer:- 37 / 216 × 57 = 2,187 / 5,12,00,00,000 = 0.00000043.

### Step-by-step solution:-

[[1/4]^{4} × [1/4]^{4}] ×[[3/5]^{12} ÷ [3/5]^{5}]

= [[1/2^{2}]^{4}]^{2} × [[3/5]^{12} ÷ [3/5]^{5}] ….......................................... (m×m = m^{2})

= [1/2]^{16} × [[3/5]^{12} ÷ [3/5]^{5}] ….............................................. [(b^{n})m = b^{nm}]

= [1^{8}/2^{16}] × [3^{12}/5^{12}] ÷ [3^{5}/5^{5}] ............................................. [a^{n}/b^{n} = (a/b)^{n}]

= [1/2^{16}] × [3^{12}/5^{12}] × [5^{5}/3^{5}] .............................................. (Taking reciprocal & 1^{n} = 1)

= [1/2^{16}] × [3^{12} ×5^{5} / 5^{12} × 3^{5}]

= [1/2^{16}] × [3^{12-5} × 5^{5-12}] ...................................................... (a^{n} / a^{m} = a^{n-m})

= [1/2^{16}] × [3^{7 }× 5^{-7}]

= [1/2^{16]} × [3^{7} / 5^{7}] ............................................................. (b^{-n} = 1 / b^{n})

= 3^{7} / 2^{16} × 5^{7}

∴ Simplifying the given expression, we get the answer:- 3^{7} / 2^{16} × 5^{7} = 2,187 / 5,12,00,00,000 = 0.00000043.

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