Question

Simplify:12^3×15^4/81×25^2​

Answer 1

Given:

An expression -

$\bf \implies \dfrac{12^3 \times 15^4}{81 \times 25^2}$

What To Find:

We have to -

• Simplify the given expression.

Solution:

$\sf \implies \dfrac{12^3 \times 15^4}{81 \times 25^2}$

The numerator can be written as,

$\sf \implies \dfrac{(3 \times 4)^3 \times (3 \times 5)^4}{81 \times 25^2}$

Again the numerator can be written as,

$\sf \implies \dfrac{(3 \times 2^2)^3 \times (3 \times 5)^4}{81 \times 25^2}$

Remove the brackets,

$\sf \implies \dfrac{3^3 \times 2^6 \times 3^4 \times 5^4}{81 \times 25^2}$

The denominator can be written as,

$\sf \implies \dfrac{3^3 \times 2^6 \times 3^4 \times 5^4}{9^2 \times (5^2)^2}$

Again the denominator can be written as,

$\sf \implies \dfrac{3^3 \times 2^6 \times 3^4 \times 5^4}{(3^2)^2 \times (5^2)^2}$

Remove the brackets,

$\sf \implies \dfrac{3^3 \times 2^6 \times 3^4 \times 5^4}{3^4 \times 5^4}$

Rearrange the values in the numerator,

$\sf \implies \dfrac{2^6 \times 3^3 \times 3^4 \times 5^4}{3^4 \times 5^4}$

Use the law in the numerator:  $\sf a^m \times a^n = a^{m+n}$

$\sf \implies \dfrac{2^6 \times 3^{3+4} \times 5^4}{3^4 \times 5^4}$

Solve,

$\sf \implies \dfrac{2^6 \times 3^{7} \times 5^4}{3^4 \times 5^4}$

Use the law:  $\sf a^m \div a^n = a^{m-n}$

$\sf \implies 2^6 \times 3^{7-4} \times 5^{4-4}$

Solve the exponents,

$\sf \implies 2^6 \times 3^{3} \times 5^{0}$

Write 5⁰ as 1,

$\sf \implies 2^6 \times 3^{3} \times 1$

Can be written as,

$\sf \implies 2^6 \times 3^{3}$

Find the powers,

$\sf \implies 64 \times 27$

Multiply,

$\sf \implies 1728$

Final Answer:

∴ Thus, the answer is 1728 after simplifying the expression.

Answer 2

Answer:

Answer is given in the picture