Question

Simplify:
2-⁴X81x5⁷
--------------
2-⁵X3²x5⁹​

Answer 1

Given:

The expression:-

$\sf \dfrac{2^{-4} \times 81 \times 5^7}{2^{-6} \times 3^2 \times 5^9}$

What To Find:

We have to simplify the expression.

Solution:

$\sf \dfrac{2^{-4} \times 81 \times 5^7}{2^{-6} \times 3^2 \times 5^9}$

81 can be written as 9²,

$\sf \Rightarrow \dfrac{2^{-4} \times 9^2 \times 5^7}{2^{-6} \times 3^2 \times 5^9}$

9² can be written as (3²)² = 3⁴,

$\sf \Rightarrow \dfrac{2^{-4} \times 3^4 \times 5^7}{2^{-6} \times 3^2 \times 5^9}$

Use $\sf a^n \div a^m = a^{n-m}$,

$\sf \Rightarrow 2^{-4 - (-6)} \times 3^{4 -2} \times 5^{7 - 9}$

Solve the exponents,

$\sf \Rightarrow 2^{2} \times 3^{2} \times 5^{- 2}$

Simplify them,

$\sf \Rightarrow 4 \times 9 \times \dfrac{1}{25}$

Multiply 4, 9 an 1,

$\sf \Rightarrow \dfrac{36}{25}$

Also written as,

$\sf \Rightarrow \bigg( \dfrac{6}{5} \bigg)^2$

∴ Hence, the answer is 36/25 or (6/5)²

Answer 2

Given:

The expression:-

$\sf \dfrac{2^{-4} \times 81 \times 5^7}{2^{-6} \times 3^2 \times 5^9}$

What To Find:

We have to simplify the expression.

Solution:

$\sf \dfrac{2^{-4} \times 81 \times 5^7}{2^{-6} \times 3^2 \times 5^9}$

81 can be written as 9²,

$\sf \Rightarrow \dfrac{2^{-4} \times 9^2 \times 5^7}{2^{-6} \times 3^2 \times 5^9}$

9² can be written as (3²)² = 3⁴,

$\sf \Rightarrow \dfrac{2^{-4} \times 3^4 \times 5^7}{2^{-6} \times 3^2 \times 5^9}$

Use $\sf a^n \div a^m = a^{n-m}$,

$\sf \Rightarrow 2^{-4 - (-6)} \times 3^{4 -2} \times 5^{7 - 9}$

Solve the exponents,

$\sf \Rightarrow 2^{2} \times 3^{2} \times 5^{- 2}$

Simplify them,

$\sf \Rightarrow 4 \times 9 \times \dfrac{1}{25}$

Multiply 4, 9 an 1,

$\sf \Rightarrow \dfrac{36}{25}$

Also written as,

$\sf \Rightarrow \bigg( \dfrac{6}{5} \bigg)^2$

∴ Hence, the answer is 36/25 or (6/5)²