Question

64^12 ÷ 4^15 = 64^x What is the value of x?

Answer 1

Answer:

Answer is 7

Step-by-step explanation:

(64)^12/4^15=64^x

(2^6)^12/(2^2)^15=(2^6)^x

2^72/2^30=2^6x

2^72-30

Since bases are same we equate the power

Therefore

72-30=6x

42=6x

42/6=x

x=7

Answer 2

Given:

${(64)}^{12} \div {(4)}^{15} = {(64)}^{x}$

To find:

The value of x.

Solution:

To answer this question, first of all, we need to make the base values of given exponents the same.

So, as given,

we have,

${(64)}^{12} \div {(4)}^{15} = {(64)}^{x}$

This can be written as

${(64)}^{12} \div {( {4}^{3} )}^{5} = {(64)}^{x}$

${(64)}^{12} \div {(64)}^{5} = {(64)}^{x} \: \: (i)$

(cube of 4 = 64)

Now,

as we know that

$\frac{ {x}^{a} }{ {x}^{b} } = {(x)}^{a - b}$

So,

(i) can be written as

${(64)}^{12 - 5} = {(64)}^{x}$

${(64)}^{7} = {(64)}^{x}$

As the base is the same, so on comparing the powers, we get,

x = 7

Hence, the value of x is 7.