Evaluate -1-43-2 -1-42-3

Using (a^m)^n=a^m× n[(1/4)^3]^2 ÷[(1/4)^2]^3= (1/4)^3× 2 ÷(1/4)^2× 3 =(1/4)^6÷(1/4)^6 By using a^m÷a^n=a^m n⇒(1/4)^6 ...

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Byju's Answer

Standard IX

Mathematics

Null Matrix

Evaluate :[1/...

Question

Evaluate :
${[{(\frac{1}{4})}^{3}]}^{2} \div {[{(\frac{1}{4})}^{2}]}^{3}$

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Solution

Using ${(a^{m})}^{n} = a^{m \times n}$
${[{(\frac{1}{4})}^{3}]}^{2} \div {[{(\frac{1}{4})}^{2}]}^{3} = {(\frac{1}{4})}^{3 \times 2} \div {(\frac{1}{4})}^{2 \times 3}$
$= {(\frac{1}{4})}^{6} \div {(\frac{1}{4})}^{6}$
By using $a^{m} \div a^{n} = a^{m - n}$
$\Rightarrow {(\frac{1}{4})}^{6 - 6} \Rightarrow {(\frac{1}{4})}^{0} = 1 (: . Z e r o p o w e r o f a n y b a s e i s 1)$
Hence, the final answer is $1 .$

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Similar questions

From the given place value table, write the decimal number.

Thousands	Hundreds	Tens	Ones	Tenths	Hundredths	Thousandths
$(1000)$	$(100)$	$(10)$	$(1)$	$(\frac{1}{10})$	$(\frac{1}{100})$	$(\frac{1}{1000})$
				$8$	$2$	$3$

From the following place value table, write the decimal number:-

Thousand	Hundred	Tens	Ones	Tenths	Hundredths	Thousandths
$(1000)$	$(100)$	$(10)$	$(1)$	$(\frac{1}{10})$	$(\frac{1}{100})$	$(\frac{1}{1000})$
			$9$	$6$

Evaluate : ${(6 \frac{2}{3})}^{2} - {(2 \frac{1}{3})}^{2}$

Find the value of $x$ so that;
$(i) {(\frac{3}{4})}^{2 x + 1} = {({(\frac{3}{4})}^{3})}^{3}$
$(i i) {(\frac{2}{5})}^{3} \times {(\frac{2}{5})}^{6} = {(\frac{2}{5})}^{3 x}$
$(i i i) {(- \frac{1}{5})}^{20} \div {(- \frac{1}{5})}^{15} = {(- \frac{1}{5})}^{5 x}$
$(i v) \frac{1}{16} \times {(\frac{1}{2})}^{2} = {(\frac{1}{2})}^{3 (x - 2)}$

Q. Evaluate

{⎡ ⎣ {({(\frac{2}{3})}^{5})}^{3} ⎤ ⎦}^{- 2}

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Evaluate :1432÷1423

Using amn=am×n1432÷1423=143×2÷142×3 =146÷146 By using am÷an=am-n⇒146-6⇒140=1(:.Zeropowerofanybaseis1)Hence, the final answer is 1.

Evaluate :
${[{(\frac{1}{4})}^{3}]}^{2} \div {[{(\frac{1}{4})}^{2}]}^{3}$