(0.25)^{6} div (0.125)^{2} times (0.5)^{4} = | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given equation: $(0.25)^{6} \div (0.125)^{2} 	imes (0.5)^{4} = (0.5)^{x+3}$Express all terms with base $0.5$:$(0.25) = (0.5)^{2}$$(0.125) = (0.5)

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(D) Given equation: $(0.25)^{6} \div (0.125)^{2} 	imes (0.5)^{4} = (0.5)^{x+3}$Express all terms with base $0.5$:$(0.25) = (0.5)^{2}$$(0.125) = (0.5)^{3}$Substitute these into the equation:$((0.5)^{2})^{6} \div ((0.5)^{3})^{2} 	imes (0.5)^{4} = (0.5)^{x+3}$Apply the power rule $(a^{m})^{n} = a^{m 	imes n}$:$(0.5)^{12} \div (0.5)^{6} 	imes (0.5)^{4} = (0.5)^{x+3}$Apply the laws of exponents $a^{m} \div a^{n} = a^{m-n}$ and $a^{m} 	imes a^{n} = a^{m+n}$:$(0.5)^{12-6+4} = (0.5)^{x+3}$$(0.5)^{10} = (0.5)^{x+3}$Since the bases are equal,equate the exponents:$10 = x + 3$$x = 10 - 3$$x = 7$

$(0.25)^{6} \div (0.125)^{2} \times (0.5)^{4} = (0.5)^{?+3}$

Similar Questions

The sum of squares of two numbers is $80$ and the square of their difference is $36$. The product of the two numbers is

If the digit in the unit's place of a two-digit number is halved and the digit in the ten's place is doubled,the number thus obtained is equal to the number obtained by interchanging the digits. Which of the following is definitely true?

$A$ two-digit number is such that the product of its digits is $8$. When $18$ is added to the number,the digits are reversed. The number is:

$9999 + 8888 + 777 + ? = 19700$

The sum of three numbers is $264$. If the first number is twice the second and the third number is one-third of the first,then the second number is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module