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

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(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$

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

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