Question

PLEASE HELP I REALLY NEED AN ANSWER ALSO ONLY ANSWER IF YOUR GOING TO GIVE A STEP BY STEP SOLUTION

Answer 1

The answer of the given expression is 80.

Exponents

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

For example:-

$5^4$ can be written as 5*5*5*5.

Here 4 is the exponent or power and 5 is the base.

There are some laws of exponents which we use while calculating the answer to such expressions.

Given expression:-

$\frac{12^7*30^5}{25^2*8^5*27^4}$

We have to simplify the given solution using the laws of exponents.

First we will divide them in their prime factors.

We know that,

$(x^a)^b=x^{ab}$

We can write,

$12^7 = (2^2)^7*3^7=2^{14}*3^7$

$30^5=2^5*3^5*5^5$

$25^2=(5^2)^2=5^4$

$8^5=(2^3)^5=2^{15}$

$27^4=(3^3)^4=3^{12}$

Hence, we can write the given expression as follows,

$\frac{2^{14}*3^7*2^5*3^5*5^5}{5^4*2^{15}*3^{12}}$

Also, we know that,

$x^a*x^b=x^{a+b}\\x^a/x^b=x^{a-b}$

We can write,

${2^{(14+5-15)}*3^{(7+5-12)}*5^{(5-4)}}$

$2^4*3^0*5^1$ = 16*1*5 = 80

To learn more about Exponent, here:-

brainly.com/question/5497425

#SPJ1